Finite Group Databasebeta

← C3×#17580 #10636187

Subgroups — C3×#17580 #10636187

Order 768.

1024 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#529C211yesmaximal, characteristic
2C3×#2920C211yesmaximal, characteristic, complemented
3C3×#2283C211yesmaximal, characteristic, complemented
4C3×#1521C214yesmaximal, complemented
5C3×#1511C212yesmaximal, complemented
6C3×#1510C212yesmaximal
7C3×#1509C214yesmaximal, complemented
8#17580C311yesmaximal, characteristic, direct product factor, Sylow
9C3×#529—21no—
10C3×#529—21no—
11C3×#529—21no—
12C3×#529—21no—
13C3×#529C412yescomplemented
14C3×#529C412yescomplemented
15C3×#529C2212yes—
16C3×#529C2212yes—
17C2×C3×#126—21no—
18C2×C3×#125C411yescharacteristic, complemented
19C2×C3×#124C411yescharacteristic, complemented
20C2×C3×#123—21no—
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×C3×#121C2211yescharacteristic
23C2×C3×C4×Q8C411yescharacteristic, complemented
24C2×C3×C4×D4—21no—
25C2×C3×C4×D4C411yescharacteristic, complemented
26C2×C3×#117—21no—
27C22×C3×C42C2211yescharacteristic
28C3×#432—21no—
29C3×#432C2212yescomplemented
30C3×#431—21no—
31C3×#431C2212yescomplemented
32C3×#423—21no—
33C3×#407C2212yes—
34C3×C4×M16—21no—
35C3×#383C2212yescomplemented
36C3×#382—21no—
37C3×#381C2212yes—
38C3×#380—21no—
39C3×C4×C4⋊C4C2212yescomplemented
40C3×C4×C22⋊C4—21no—
41C3×#376—21no—
42C3×#328C2218yescomplemented
43C3×#327C2218yes—
44C2×#529C2×C311yescharacteristic
45#2920C2×C311yescharacteristic, complemented
46#2283C2×C311yescharacteristic, complemented
47#1521C2×C314yescomplemented
48#1511C2×C312yescomplemented
49#1510C2×C312yes—
50#1509C2×C314yescomplemented
51C22×C3×Q8C2×C411yescharacteristic
52C22×C3×D4—21no—
53C22×C3×D4C2×C411yescharacteristic
54C23×C3×C4—21no—
55C23×C3×C4D411yescharacteristic
56C23×C3×C4D411yescharacteristic
57C23×C3×C4C2311yescharacteristic
58C2×C3×M16—22no—
59C3×#126—22no—
60C3×#126—22no—
61C3×#126—22no—
62C3×#126—22no—
63C3×#125—21no—
64C3×#125—21no—
65C3×#125C2×C412yes—
66C3×#125C2×C412yes—
67C3×#124—21no—
68C3×#124—21no—
69C3×#124C2×C412yes—
70C3×#124C2×C412yes—
71C3×#123—22no—
72C3×#123—22no—
73C3×#123—22no—
74C3×#123—22no—
75C3×C22⋊Q8—21no—
76C3×C22⋊Q8—21no—
77C3×C22⋊Q8C2×C412yes—
78C3×C22⋊Q8C2312yes—
79C3×#121—21no—
80C3×#121—21no—
81C3×#121C2×C412yes—
82C3×#121C2312yes—
83C3×C4×Q8—21no—
84C3×C4×Q8—21no—
85C3×C4×Q8C2×C412yes—
86C3×C4×Q8C2×C412yes—
87C3×C4×D4—22no—
88C3×C4×D4—22no—
89C3×C4×D4—22no—
90C3×C4×D4—22no—
91C3×C4×D4—21no—
92C3×C4×D4—21no—
93C3×C4×D4C2×C412yes—
94C3×C4×D4C2×C412yes—
95C3×#117—22no—
96C3×#117—22no—
97C3×#117—22no—
98C3×#117—22no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—22no—
104C2×C3×C4⋊C4C2×C411yescharacteristic
105C2×C3×C4⋊C4C2×C411yescharacteristic
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—22no—
112C2×C3×C42—21no—
113C2×C3×C42—22no—
114C2×C3×C42C2×C411yescharacteristic
115C2×C3×C42C2×C411yescharacteristic
116C2×C3×C42C2×C411yescharacteristic
117C2×C3×C42C2×C411yescharacteristic
118C2×C3×C42D411yescharacteristic
119C2×C3×C42D411yescharacteristic
120C2×C3×C42D411yescharacteristic
121C2×C3×C42D411yescharacteristic
122C2×C3×C42D411yescharacteristic
123C2×C3×C42D411yescharacteristic
124C2×C3×C42C2311yescharacteristic
125C2×C3×C42C2311yescharacteristic
126C3×C4⋊C8—22no—
127C3×C4⋊C8—22no—
128C3×C22⋊C8—22no—
129C3×C22⋊C8C2314yes—
130C3×#97—22no—
131C3×C4×C8—22no—
132C3×#95—22no—
133C3×#95—22no—
134C3×#95—22no—
135C3×#95C2314yes—
136#529—21no—
137#529—21no—
138#529—21no—
139#529—21no—
140#529C3×C412yescomplemented
141#529C3×C412yescomplemented
142#529C22×C312yes—
143#529C22×C312yes—
144C2×#126—21no—
145C2×#125C3×C411yescharacteristic, complemented
146C2×#124C3×C411yescharacteristic, complemented
147C2×#123—21no—
148C2×C22⋊Q8C22×C311yescharacteristic
149C2×#121C22×C311yescharacteristic
150C2×C4×Q8C3×C411yescharacteristic, complemented
151C2×C4×D4—21no—
152C2×C4×D4C3×C411yescharacteristic, complemented
153C2×#117—21no—
154C22×C42C22×C311yescharacteristic
155#432—21no—
156#432C22×C312yescomplemented
157#431—21no—
158#431C22×C312yescomplemented
159#423—21no—
160#407C22×C312yes—
161C4×M16—21no—
162#383C22×C312yescomplemented
163#382—21no—
164#381C22×C312yes—
165#380—21no—
166C4×C4⋊C4C22×C312yescomplemented
167C4×C22⋊C4—21no—
168#376—21no—
169#328C22×C318yescomplemented
170#327C22×C318yes—
171C24×C3—21no—
172C24×C3C2×D411yescharacteristic
173C2×C3×Q8—21no—
174C2×C3×Q8—42no—
175C2×C3×Q8C22×C412yes—
176C2×C3×D4—22no—
177C2×C3×D4—22no—
178C2×C3×D4—21no—
179C2×C3×D4—42no—
180C2×C3×D4—44no—
181C2×C3×D4C22×C412yes—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—24no—
188C22×C3×C4—42no—
189C22×C3×C4—42no—
190C22×C3×C4—42no—
191C22×C3×C4—44no—
192C22×C3×C4C22⋊C411yescharacteristic
193C22×C3×C4C22⋊C411yescharacteristic
194C22×C3×C4C22⋊C411yescharacteristic
195C22×C3×C4C22⋊C411yescharacteristic
196C22×C3×C4C22⋊C411yescharacteristic
197C22×C3×C4C22⋊C411yescharacteristic
198C22×C3×C4C22⋊C411yescharacteristic
199C22×C3×C4C22⋊C411yescharacteristic
200C22×C3×C4C22×C411yescharacteristic
201C22×C3×C4C22×C411yescharacteristic
202C22×C3×C4C2×D411yescharacteristic
203C22×C3×C4C2×D411yescharacteristic
204C22×C3×C4C2×D411yescharacteristic
205C22×C3×C4C2×D411yescharacteristic
206C22×C3×C4C2×D411yescharacteristic
207C22×C3×C4C2×D411yescharacteristic
208C22×C3×C4C2×D411yescharacteristic
209C22×C3×C4C2411yescharacteristic
210C3×M16—44no—
211C2×C3×C8—24no—
212C3×C4⋊C4—22no—
213C3×C4⋊C4—22no—
214C3×C4⋊C4—22no—
215C3×C4⋊C4—22no—
216C3×C4⋊C4—22no—
217C3×C4⋊C4—22no—
218C3×C4⋊C4—22no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—22no—
222C3×C4⋊C4—44no—
223C3×C4⋊C4C22×C412yes—
224C3×C4⋊C4C22×C412yes—
225C3×C22⋊C4—22no—
226C3×C22⋊C4—22no—
227C3×C22⋊C4—22no—
228C3×C22⋊C4—22no—
229C3×C22⋊C4—22no—
230C3×C22⋊C4—22no—
231C3×C22⋊C4—22no—
232C3×C22⋊C4—22no—
233C3×C22⋊C4—22no—
234C3×C22⋊C4—22no—
235C3×C22⋊C4—44no—
236C3×C42—22no—
237C3×C42—22no—
238C3×C42—44no—
239C3×C42C22⋊C411yescharacteristic
240C3×C42C22⋊C411yescharacteristic
241C3×C42C22⋊C411yescharacteristic
242C3×C42C22⋊C411yescharacteristic
243C3×C42C22⋊C411yescharacteristic
244C3×C42C22⋊C411yescharacteristic
245C3×C42C22⋊C411yescharacteristic
246C3×C42C22⋊C411yescharacteristic
247C3×C42C22×C411yescharacteristic
248C3×C42C22×C411yescharacteristic
249C3×C42C22×C411yescharacteristic
250C3×C42C22×C411yescharacteristic
251C3×C42C2×D411yescharacteristic
252C3×C42C2×D411yescharacteristic
253C3×C42C2×D411yescharacteristic
254C3×C42C2×D411yescharacteristic
255C22×Q8C2×C3×C411yescharacteristic
256C22×D4—21no—
257C22×D4C2×C3×C411yescharacteristic
258C23×C4—21no—
259C23×C4C3×D411yescharacteristic
260C23×C4C3×D411yescharacteristic
261C23×C4C23×C311yescharacteristic
262C2×M16—22no—
263#126—22no—
264#126—22no—
265#126—22no—
266#126—22no—
267#125—21no—
268#125—21no—
269#125C2×C3×C412yes—
270#125C2×C3×C412yes—
271#124—21no—
272#124—21no—
273#124C2×C3×C412yes—
274#124C2×C3×C412yes—
275#123—22no—
276#123—22no—
277#123—22no—
278#123—22no—
279C22⋊Q8—21no—
280C22⋊Q8—21no—
281C22⋊Q8C2×C3×C412yes—
282C22⋊Q8C23×C312yes—
283#121—21no—
284#121—21no—
285#121C2×C3×C412yes—
286#121C23×C312yes—
287C4×Q8—21no—
288C4×Q8—21no—
289C4×Q8C2×C3×C412yes—
290C4×Q8C2×C3×C412yes—
291C4×D4—22no—
292C4×D4—22no—
293C4×D4—22no—
294C4×D4—22no—
295C4×D4—21no—
296C4×D4—21no—
297C4×D4C2×C3×C412yes—
298C4×D4C2×C3×C412yes—
299#117—22no—
300#117—22no—
301#117—22no—
302#117—22no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4C2×C3×C411yescharacteristic
309C2×C4⋊C4C2×C3×C411yescharacteristic
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—22no—
316C2×C42—21no—
317C2×C42—22no—
318C2×C42C2×C3×C411yescharacteristic
319C2×C42C2×C3×C411yescharacteristic
320C2×C42C2×C3×C411yescharacteristic
321C2×C42C2×C3×C411yescharacteristic
322C2×C42C3×D411yescharacteristic
323C2×C42C3×D411yescharacteristic
324C2×C42C3×D411yescharacteristic
325C2×C42C3×D411yescharacteristic
326C2×C42C3×D411yescharacteristic
327C2×C42C3×D411yescharacteristic
328C2×C42C23×C311yescharacteristic
329C2×C42C23×C311yescharacteristic
330C4⋊C8—22no—
331C4⋊C8—22no—
332C22⋊C8—22no—
333C22⋊C8C23×C314yes—
334#97—22no—
335C4×C8—22no—
336#95—22no—
337#95—22no—
338#95—22no—
339#95C23×C314yes—
340C23×C3—22no—
341C23×C3—22no—
342C23×C3—22no—
343C23×C3—41no—
344C23×C3—42no—
345C23×C3—42no—
346C23×C3—42no—
347C23×C3C2×C22⋊C411yescharacteristic
348C23×C3C2×C22⋊C411yescharacteristic
349C23×C3C22×D411yescharacteristic
350C3×Q8—42no—
351C3×Q8—42no—
352C3×D4—42no—
353C3×D4—42no—
354C3×D4—44no—
355C3×D4—44no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—41no—
367C2×C3×C4—41no—
368C2×C3×C4—41no—
369C2×C3×C4—41no—
370C2×C3×C4—41no—
371C2×C3×C4—41no—
372C2×C3×C4—41no—
373C2×C3×C4—41no—
374C2×C3×C4—41no—
375C2×C3×C4—41no—
376C2×C3×C4—41no—
377C2×C3×C4—44no—
378C2×C3×C4—42no—
379C2×C3×C4—42no—
380C2×C3×C4—42no—
381C2×C3×C4—44no—
382C2×C3×C4—44no—
383C2×C3×C4—44no—
384C2×C3×C4—44no—
385C2×C3×C4C2×C22⋊C411yescharacteristic
386C2×C3×C4C2×C22⋊C411yescharacteristic
387C2×C3×C4C2×C22⋊C411yescharacteristic
388C2×C3×C4C2×C22⋊C411yescharacteristic
389C2×C3×C4C2×C22⋊C411yescharacteristic
390C2×C3×C4C2×C22⋊C411yescharacteristic
391C2×C3×C4C2×C22⋊C411yescharacteristic
392C2×C3×C4C2×C22⋊C411yescharacteristic
393C2×C3×C4C2×C22⋊C411yescharacteristic
394C2×C3×C4C2×C22⋊C411yescharacteristic
395C2×C3×C4C23×C411yescharacteristic
396C2×C3×C4C22×D411yescharacteristic
397C3×C8—44no—
398C24—21no—
399C24C2×C3×D411yescharacteristic
400C2×Q8—21no—
401C2×Q8—42no—
402C2×Q8C22×C3×C412yes—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—21no—
406C2×D4—42no—
407C2×D4—44no—
408C2×D4C22×C3×C412yes—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—44no—
419C22×C4C3×C22⋊C411yescharacteristic
420C22×C4C3×C22⋊C411yescharacteristic
421C22×C4C3×C22⋊C411yescharacteristic
422C22×C4C3×C22⋊C411yescharacteristic
423C22×C4C3×C22⋊C411yescharacteristic
424C22×C4C3×C22⋊C411yescharacteristic
425C22×C4C3×C22⋊C411yescharacteristic
426C22×C4C3×C22⋊C411yescharacteristic
427C22×C4C22×C3×C411yescharacteristic
428C22×C4C22×C3×C411yescharacteristic
429C22×C4C2×C3×D411yescharacteristic
430C22×C4C2×C3×D411yescharacteristic
431C22×C4C2×C3×D411yescharacteristic
432C22×C4C2×C3×D411yescharacteristic
433C22×C4C2×C3×D411yescharacteristic
434C22×C4C2×C3×D411yescharacteristic
435C22×C4C2×C3×D411yescharacteristic
436C22×C4C24×C311yescharacteristic
437M16—44no—
438C2×C8—24no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—44no—
450C4⋊C4C22×C3×C412yes—
451C4⋊C4C22×C3×C412yes—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—44no—
463C42—22no—
464C42—22no—
465C42—44no—
466C42C3×C22⋊C411yescharacteristic
467C42C3×C22⋊C411yescharacteristic
468C42C3×C22⋊C411yescharacteristic
469C42C3×C22⋊C411yescharacteristic
470C42C3×C22⋊C411yescharacteristic
471C42C3×C22⋊C411yescharacteristic
472C42C3×C22⋊C411yescharacteristic
473C42C3×C22⋊C411yescharacteristic
474C42C22×C3×C411yescharacteristic
475C42C22×C3×C411yescharacteristic
476C42C22×C3×C411yescharacteristic
477C42C22×C3×C411yescharacteristic
478C42C2×C3×D411yescharacteristic
479C42C2×C3×D411yescharacteristic
480C42C2×C3×D411yescharacteristic
481C42C2×C3×D411yescharacteristic
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—21no—
488C22×C3—21no—
489C22×C3—44no—
490C22×C3—42no—
491C22×C3—42no—
492C22×C3—42no—
493C22×C3—84no—
494C22×C3#41012yes—
495C22×C3C22×C22⋊C411yescharacteristic
496C22×C3#57512yes—
497C3×C4—21no—
498C3×C4—21no—
499C3×C4—21no—
500C3×C4—21no—
501C3×C4—21no—
502C3×C4—21no—
503C3×C4—21no—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—42no—
509C3×C4—42no—
510C3×C4—42no—
511C3×C4—84no—
512C3×C4#42112yes—
513C23—22no—
514C23—22no—
515C23—22no—
516C23—41no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23C2×C3×C22⋊C411yescharacteristic
521C23C2×C3×C22⋊C411yescharacteristic
522C23C22×C3×D411yescharacteristic
523Q8—42no—
524Q8—42no—
525D4—42no—
526D4—42no—
527D4—44no—
528D4—44no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—44no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—44no—
555C2×C4—44no—
556C2×C4—44no—
557C2×C4—44no—
558C2×C4C2×C3×C22⋊C411yescharacteristic
559C2×C4C2×C3×C22⋊C411yescharacteristic
560C2×C4C2×C3×C22⋊C411yescharacteristic
561C2×C4C2×C3×C22⋊C411yescharacteristic
562C2×C4C2×C3×C22⋊C411yescharacteristic
563C2×C4C2×C3×C22⋊C411yescharacteristic
564C2×C4C2×C3×C22⋊C411yescharacteristic
565C2×C4C2×C3×C22⋊C411yescharacteristic
566C2×C4C2×C3×C22⋊C411yescharacteristic
567C2×C4C2×C3×C22⋊C411yescharacteristic
568C2×C4C23×C3×C411yescharacteristic
569C2×C4C22×C3×D411yescharacteristic
570C8—44no—
571C2×C3—22no—
572C2×C3—22no—
573C2×C3—41no—
574C2×C3—82no—
575C2×C3C2×#41011yescharacteristic
576C2×C3#289611yescharacteristic
577C2×C3C2×#42111yescharacteristic
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—44no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—84no—
590C22C3×#41012yes—
591C22C22×C3×C22⋊C411yescharacteristic
592C22C3×#57512yes—
593C4—21no—
594C4—21no—
595C4—21no—
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—21no—
601C4—21no—
602C4—21no—
603C4—21no—
604C4—42no—
605C4—42no—
606C4—42no—
607C4—84no—
608C4C3×#42112yes—
609C3#1758011yescharacteristic, direct product factor, Sylow
610C2—22no—
611C2—22no—
612C2—41no—
613C2—82no—
614C2C2×C3×#41011yescharacteristic
615C2C3×#289611yescharacteristic
616C2C2×C3×#42111yescharacteristic
subgroupG/H
center, socleC22×C3C22×C22⋊C4
commutatorC2×C4C23×C3×C4
Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#121C22
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ C22×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#2920C2semidirect
3. C3×#2283C2semidirect
4. C3×#1521C2semidirect
5. C3×#1511C2semidirect
7. C3×#1509C2semidirect
8. #17580C3direct (N × H)
13. C3×#529C4semidirect
14. C3×#529C4semidirect
18. C2×C3×#125C4semidirect
19. C2×C3×#124C4semidirect
23. C2×C3×C4×Q8C4semidirect
25. C2×C3×C4×D4C4semidirect
29. C3×#432C22semidirect
31. C3×#431C22semidirect
35. C3×#383C22semidirect
39. C3×C4×C4⋊C4C22semidirect
42. C3×#328C22semidirect
45. #2920C2×C3semidirect
46. #2283C2×C3semidirect
47. #1521C2×C3semidirect
48. #1511C2×C3semidirect
50. #1509C2×C3semidirect
140. #529C3×C4semidirect
141. #529C3×C4semidirect
145. C2×#125C3×C4semidirect
146. C2×#124C3×C4semidirect
150. C2×C4×Q8C3×C4semidirect
152. C2×C4×D4C3×C4semidirect
156. #432C22×C3semidirect
158. #431C22×C3semidirect
162. #383C22×C3semidirect
166. C4×C4⋊C4C22×C3semidirect
169. #328C22×C3semidirect
609. C3#17580direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5292
C3×#29202
C3×#22832
C3×#15212
C3×#15112
C3×#15102
C3×#15092
#175803