Finite Group Databasebeta

← C3×#24684 #10643291

Subgroups — C3×#24684 #10643291

Order 768.

826 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#478C211yesmaximal, characteristic, complemented
2C2×C3×C4×D8C211yesmaximal, characteristic
3C3×#2566C211yesmaximal, characteristic, complemented
4C3×#2357C211yesmaximal, characteristic, complemented
5C3×#2073C211yesmaximal, characteristic, complemented
6C3×#2071C211yesmaximal, characteristic, complemented
7C3×#2054C211yesmaximal, characteristic
8C3×#2054C211yesmaximal, characteristic
9C3×#1991C211yesmaximal, characteristic, complemented
10C3×#1949C211yesmaximal, characteristic, complemented
11C3×#1947C211yesmaximal, characteristic, complemented
12C3×#1939C211yesmaximal, characteristic, complemented
13C3×#1926C211yesmaximal, characteristic, complemented
14C3×#1925C211yesmaximal, characteristic, complemented
15C3×#1804C211yesmaximal, characteristic, complemented
16#24684C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×D8C2211yescharacteristic
18C2×C3×#125C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C3×#478—24no—
22C3×C4×D8—24no—
23C2×C3×#107C2211yescharacteristic
24C2×C3×#107C2211yescharacteristic
25C2×C3×#106C2211yescharacteristic
26C2×C3×C4⋊C8C2211yescharacteristic
27C2×C3×C4⋊C8C2211yescharacteristic
28C2×C3×C4⋊C8C2211yescharacteristic
29C2×C3×#102C2211yescharacteristic
30C2×C3×#102C2211yescharacteristic
31C2×C3×#102C2211yescharacteristic
32C2×C3×#102C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×C4×C8C2211yescharacteristic
36C3×#396—21no—
37C3×#396—21no—
38C3×#390C2211yescharacteristic
39C3×#390C2211yescharacteristic
40C3×#390C2211yescharacteristic
41C3×#390C2211yescharacteristic
42C3×#388—21no—
43C3×#388—21no—
44C3×#385—21no—
45C3×#385—21no—
46C3×#384C2211yescharacteristic
47C3×#382C2211yescharacteristic
48C3×#382C2211yescharacteristic
49C3×#381—21no—
50C3×C4×C4⋊C4C2211yescharacteristic
51C3×C4×C4⋊C4C2211yescharacteristic
52C3×C4×C4⋊C4C2211yescharacteristic
53C3×C4×C22⋊C4—21no—
54C3×#340C2211yescharacteristic
55C3×#340C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C2×#478C2×C311yescharacteristic, complemented
63C2×C4×D8C2×C311yescharacteristic
64#2566C2×C311yescharacteristic, complemented
65#2357C2×C311yescharacteristic, complemented
66#2073C2×C311yescharacteristic, complemented
67#2071C2×C311yescharacteristic, complemented
68#2054C2×C311yescharacteristic
69#2054C2×C311yescharacteristic
70#1991C2×C311yescharacteristic, complemented
71#1949C2×C311yescharacteristic, complemented
72#1947C2×C311yescharacteristic, complemented
73#1939C2×C311yescharacteristic, complemented
74#1926C2×C311yescharacteristic, complemented
75#1925C2×C311yescharacteristic, complemented
76#1804C2×C311yescharacteristic, complemented
77C22×C3×D4C2311yescharacteristic
78C22×C3×D4C2311yescharacteristic
79C23×C3×C4—21no—
80C23×C3×C4—21no—
81C2×C3×D8—22no—
82C2×C3×D8—22no—
83C2×C3×D8—22no—
84C22×C3×C8C2311yescharacteristic
85C22×C3×C8C2311yescharacteristic
86C22×C3×C8C2311yescharacteristic
87C22×C3×C8C2311yescharacteristic
88C3×#125—22no—
89C3×#125—22no—
90C3×C4×D4—22no—
91C3×C4×D4—22no—
92C3×C4×D4—22no—
93C3×C4×D4D414yes—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4D411yescharacteristic
99C2×C3×C4⋊C4D411yescharacteristic
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C22⋊C4—21no—
107C2×C3×C22⋊C4—21no—
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4—21no—
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C42—21no—
117C2×C3×C42—21no—
118C2×C3×C42C2311yescharacteristic
119C2×C3×C42C2311yescharacteristic
120C2×C3×C42C2311yescharacteristic
121C3×#107—22no—
122C3×#107—22no—
123C3×#106—22no—
124C3×C4⋊C8—22no—
125C3×C4⋊C8—22no—
126C3×C4⋊C8—22no—
127C3×#102—22no—
128C3×#102—22no—
129C3×#102—22no—
130C3×#102—22no—
131C3×#102—22no—
132C3×#102—22no—
133C3×C4×C8—22no—
134C3×#95—21no—
135C3×#95—21no—
136C3×#95—21no—
137C3×#95—21no—
138C3×#95—21no—
139C3×#95—21no—
140C3×#95D411yescharacteristic
141C3×#95D411yescharacteristic
142C22×D8C22×C311yescharacteristic
143C2×#125C22×C311yescharacteristic
144C2×C4×D4C22×C311yescharacteristic
145C2×C4×D4C22×C311yescharacteristic
146#478—24no—
147C4×D8—24no—
148C2×#107C22×C311yescharacteristic
149C2×#107C22×C311yescharacteristic
150C2×#106C22×C311yescharacteristic
151C2×C4⋊C8C22×C311yescharacteristic
152C2×C4⋊C8C22×C311yescharacteristic
153C2×C4⋊C8C22×C311yescharacteristic
154C2×#102C22×C311yescharacteristic
155C2×#102C22×C311yescharacteristic
156C2×#102C22×C311yescharacteristic
157C2×#102C22×C311yescharacteristic
158C2×#102C22×C311yescharacteristic
159C2×#102C22×C311yescharacteristic
160C2×C4×C8C22×C311yescharacteristic
161#396—21no—
162#396—21no—
163#390C22×C311yescharacteristic
164#390C22×C311yescharacteristic
165#390C22×C311yescharacteristic
166#390C22×C311yescharacteristic
167#388—21no—
168#388—21no—
169#385—21no—
170#385—21no—
171#384C22×C311yescharacteristic
172#382C22×C311yescharacteristic
173#382C22×C311yescharacteristic
174#381—21no—
175C4×C4⋊C4C22×C311yescharacteristic
176C4×C4⋊C4C22×C311yescharacteristic
177C4×C4⋊C4C22×C311yescharacteristic
178C4×C22⋊C4—21no—
179#340C22×C311yescharacteristic
180#340C22×C311yescharacteristic
181#340C22×C311yescharacteristic
182#340C22×C311yescharacteristic
183#340C22×C311yescharacteristic
184#340C22×C311yescharacteristic
185#336C22×C311yescharacteristic
186#336C22×C311yescharacteristic
187C24×C3—21no—
188C24×C3—21no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4—21no—
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4—21no—
199C2×C3×D4C2×D412yes—
200C2×C3×D4#4112yes—
201C22×C3×C4—21no—
202C22×C3×C4—24no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—42no—
209C22×C3×C4—81no—
210C22×C3×C4—81no—
211C22×C3×C4—81no—
212C22×C3×C4—81no—
213C22×C3×C4C2×D411yescharacteristic
214C22×C3×C4C2×D411yescharacteristic
215C22×C3×C4C2×D411yescharacteristic
216C22×C3×C4C2×D411yescharacteristic
217C22×C3×C4C2×D411yescharacteristic
218C22×C3×C4C2×D411yescharacteristic
219C22×C3×C4C2411yescharacteristic
220C3×D8—28no—
221C2×C3×C8—21no—
222C2×C3×C8—21no—
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8—21no—
226C2×C3×C8—21no—
227C2×C3×C8—21no—
228C2×C3×C8—21no—
229C2×C3×C8—21no—
230C2×C3×C8—21no—
231C2×C3×C8—21no—
232C2×C3×C8#4112yes—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—21no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—41no—
246C3×C4⋊C4—42no—
247C3×C4⋊C4—42no—
248C3×C4⋊C4—81no—
249C3×C4⋊C4—81no—
250C3×C4⋊C4C2×D412yes—
251C3×C22⋊C4—24no—
252C3×C22⋊C4—42no—
253C3×C22⋊C4—42no—
254C3×C22⋊C4—42no—
255C3×C22⋊C4—42no—
256C3×C22⋊C4—42no—
257C3×C22⋊C4—81no—
258C3×C22⋊C4—81no—
259C3×C22⋊C4—81no—
260C3×C22⋊C4—81no—
261C3×C42—21no—
262C3×C42—21no—
263C3×C42—21no—
264C3×C42—21no—
265C3×C42—81no—
266C3×C42—81no—
267C3×C42C2×D412yes—
268C3×C42#4112yes—
269C22×D4C23×C311yescharacteristic
270C22×D4C23×C311yescharacteristic
271C23×C4—21no—
272C23×C4—21no—
273C2×D8—22no—
274C2×D8—22no—
275C2×D8—22no—
276C22×C8C23×C311yescharacteristic
277C22×C8C23×C311yescharacteristic
278C22×C8C23×C311yescharacteristic
279C22×C8C23×C311yescharacteristic
280#125—22no—
281#125—22no—
282C4×D4—22no—
283C4×D4—22no—
284C4×D4—22no—
285C4×D4C3×D414yes—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4C3×D411yescharacteristic
291C2×C4⋊C4C3×D411yescharacteristic
292C2×C4⋊C4C23×C311yescharacteristic
293C2×C4⋊C4C23×C311yescharacteristic
294C2×C4⋊C4C23×C311yescharacteristic
295C2×C4⋊C4C23×C311yescharacteristic
296C2×C4⋊C4C23×C311yescharacteristic
297C2×C4⋊C4C23×C311yescharacteristic
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C42—21no—
309C2×C42—21no—
310C2×C42C23×C311yescharacteristic
311C2×C42C23×C311yescharacteristic
312C2×C42C23×C311yescharacteristic
313#107—22no—
314#107—22no—
315#106—22no—
316C4⋊C8—22no—
317C4⋊C8—22no—
318C4⋊C8—22no—
319#102—22no—
320#102—22no—
321#102—22no—
322#102—22no—
323#102—22no—
324#102—22no—
325C4×C8—22no—
326#95—21no—
327#95—21no—
328#95—21no—
329#95—21no—
330#95—21no—
331#95—21no—
332#95C3×D411yescharacteristic
333#95C3×D411yescharacteristic
334C23×C3—22no—
335C23×C3—22no—
336C23×C3—41no—
337C23×C3—41no—
338C23×C3—41no—
339C23×C3—41no—
340C23×C3—41no—
341C23×C3—41no—
342C23×C3—41no—
343C23×C3—41no—
344C23×C3—41no—
345C23×C3—41no—
346C23×C3—41no—
347C23×C3—41no—
348C23×C3C22×D411yescharacteristic
349C3×D4—22no—
350C3×D4—22no—
351C3×D4—22no—
352C3×D4—22no—
353C3×D4—41no—
354C3×D4—41no—
355C3×D4—41no—
356C3×D4—41no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—22no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—41no—
374C2×C3×C4—41no—
375C2×C3×C4—41no—
376C2×C3×C4—41no—
377C2×C3×C4—41no—
378C2×C3×C4—41no—
379C2×C3×C4—41no—
380C2×C3×C4—41no—
381C2×C3×C4—41no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—84no—
391C2×C3×C4—84no—
392C2×C3×C4#12112yes—
393C2×C3×C4#12112yes—
394C2×C3×C4#13512yes—
395C2×C3×C4C22×D411yescharacteristic
396C2×C3×C4C2×#4111yescharacteristic
397C2×C3×C4C2×#4111yescharacteristic
398C2×C3×C4C2×#4111yescharacteristic
399C2×C3×C42−1+411yescharacteristic
400C2×C3×C42−1+411yescharacteristic
401C3×C8—22no—
402C3×C8—41no—
403C3×C8—41no—
404C3×C8—41no—
405C24—21no—
406C24—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4C2×C3×D412yes—
418C2×D4C3×#4112yes—
419C22×C4—21no—
420C22×C4—24no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—42no—
427C22×C4—81no—
428C22×C4—81no—
429C22×C4—81no—
430C22×C4—81no—
431C22×C4C2×C3×D411yescharacteristic
432C22×C4C2×C3×D411yescharacteristic
433C22×C4C2×C3×D411yescharacteristic
434C22×C4C2×C3×D411yescharacteristic
435C22×C4C2×C3×D411yescharacteristic
436C22×C4C2×C3×D411yescharacteristic
437C22×C4C24×C311yescharacteristic
438D8—28no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8C3×#4112yes—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—41no—
464C4⋊C4—42no—
465C4⋊C4—42no—
466C4⋊C4—81no—
467C4⋊C4—81no—
468C4⋊C4C2×C3×D412yes—
469C22⋊C4—24no—
470C22⋊C4—42no—
471C22⋊C4—42no—
472C22⋊C4—42no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—81no—
476C22⋊C4—81no—
477C22⋊C4—81no—
478C22⋊C4—81no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—81no—
484C42—81no—
485C42C2×C3×D412yes—
486C42C3×#4112yes—
487C22×C3—42no—
488C22×C3—42no—
489C22×C3—42no—
490C22×C3—42no—
491C22×C3—42no—
492C22×C3—42no—
493C22×C3—81no—
494C22×C3—81no—
495C22×C3—81no—
496C22×C3—81no—
497C22×C3—81no—
498C22×C3—81no—
499C22×C3—81no—
500C22×C3—81no—
501C22×C3C2×#12111yescharacteristic
502C22×C3#54711yescharacteristic
503C22×C3#54811yescharacteristic
504C22×C3C2×#13511yescharacteristic
505C22×C3#57511yescharacteristic
506C22×C3#57611yescharacteristic
507C22×C3#57611yescharacteristic
508C3×C4—22no—
509C3×C4—22no—
510C3×C4—22no—
511C3×C4—41no—
512C3×C4—41no—
513C3×C4—41no—
514C3×C4—42no—
515C3×C4—81no—
516C3×C4—81no—
517C3×C4—81no—
518C3×C4—81no—
519C3×C4—81no—
520C3×C4#52511yescharacteristic
521C3×C4#53611yescharacteristic
522C3×C4#55211yescharacteristic
523C3×C4#55611yescharacteristic
524C23—22no—
525C23—22no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23C22×C3×D411yescharacteristic
539D4—22no—
540D4—22no—
541D4—22no—
542D4—22no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—84no—
581C2×C4—84no—
582C2×C4C3×#12112yes—
583C2×C4C3×#12112yes—
584C2×C4C3×#13512yes—
585C2×C4C22×C3×D411yescharacteristic
586C2×C4C2×C3×#4111yescharacteristic
587C2×C4C2×C3×#4111yescharacteristic
588C2×C4C2×C3×#4111yescharacteristic
589C2×C4C3×2−1+411yescharacteristic
590C2×C4C3×2−1+411yescharacteristic
591C8—22no—
592C8—41no—
593C8—41no—
594C8—41no—
595C2×C3—82no—
596C2×C3—82no—
597C2×C3#241511yescharacteristic
598C2×C3#303511yescharacteristic
599C2×C3#304111yescharacteristic
600C2×C3#333911yescharacteristic
601C2×C3#335511yescharacteristic
602C2×C3#336111yescharacteristic
603C2×C3#337011yescharacteristic
604C22—42no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22C2×C3×#12111yescharacteristic
619C22C3×#54711yescharacteristic
620C22C3×#54811yescharacteristic
621C22C2×C3×#13511yescharacteristic
622C22C3×#57511yescharacteristic
623C22C3×#57611yescharacteristic
624C22C3×#57611yescharacteristic
625C4—22no—
626C4—22no—
627C4—22no—
628C4—42no—
629C4—41no—
630C4—41no—
631C4—41no—
632C4—81no—
633C4—81no—
634C4—81no—
635C4—81no—
636C4—81no—
637C4C3×#52511yescharacteristic
638C4C3×#53611yescharacteristic
639C4C3×#55211yescharacteristic
640C4C3×#55611yescharacteristic
641C3#2468411yescharacteristic, direct product factor, Sylow
642C2—82no—
643C2—82no—
644C2C3×#241511yescharacteristic
645C2C3×#303511yescharacteristic
646C2C3×#304111yescharacteristic
647C2C3×#333911yescharacteristic
648C2C3×#335511yescharacteristic
649C2C3×#336111yescharacteristic
650C2C3×#337011yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C4⋊C4 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C3×#478C2semidirect
3. C3×#2566C2semidirect
4. C3×#2357C2semidirect
5. C3×#2073C2semidirect
6. C3×#2071C2semidirect
9. C3×#1991C2semidirect
10. C3×#1949C2semidirect
11. C3×#1947C2semidirect
12. C3×#1939C2semidirect
13. C3×#1926C2semidirect
14. C3×#1925C2semidirect
15. C3×#1804C2semidirect
16. #24684C3direct (N × H)
62. C2×#478C2×C3semidirect
64. #2566C2×C3semidirect
65. #2357C2×C3semidirect
66. #2073C2×C3semidirect
67. #2071C2×C3semidirect
70. #1991C2×C3semidirect
71. #1949C2×C3semidirect
72. #1947C2×C3semidirect
73. #1939C2×C3semidirect
74. #1926C2×C3semidirect
75. #1925C2×C3semidirect
76. #1804C2×C3semidirect
641. C3#24684direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×#4782
C2×C3×C4×D82
C3×#25662
C3×#23572
C3×#20732
C3×#20712
C3×#20542
C3×#19912
C3×#19492
C3×#19472
C3×#19392
C3×#19262
C3×#19252
C3×#18042
#246843