Finite Group Databasebeta

← C2×#10595270 #11901105

Subgroups — C2×#10595270 #11901105

Order 1152.

3195 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic
2C23×#627C211yesmaximal, characteristic, complemented
3C2×#64144C211yesmaximal, characteristic, complemented
4C2×C3×#935C211yesmaximal, characteristic, complemented
5C2×#63964C212yesmaximal, complemented
6C2×#63962C211yesmaximal, characteristic, complemented
7C2×#63961C211yesmaximal, characteristic, complemented
8C2×#63959C212yesmaximal, complemented
9C2×#63955C211yesmaximal, characteristic, complemented
10#10595270C2116yesmaximal, direct product factor
11C2×#63851C212yesmaximal, complemented
12C2×#63839C212yesmaximal, complemented
13C2×#5825—31nomaximal
14C2×#5648—31nomaximal
15C22×C32×D4C2211yescharacteristic
16C23×C3⋊Dic3C2211yescharacteristic
17C22×C3×#67C2211yescharacteristic
18C22×C3×#67C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C2×C3×#237—28no—
23C2×C3×#237C2218yes—
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×Dic6C2211yescharacteristic
26C22×#627—28no—
27C22×#627C2212yes—
28C22×#627C2212yes—
29C22×#627C2218yescomplemented
30C2×#3757C2211yescharacteristic
31C2×#3757C2212yes—
32#64144C2218yescomplemented
33C2×#3750C2212yes—
34C2×C3×#217C2211yescharacteristic
35C2×C3×#217C2212yes—
36C3×#935C2218yescomplemented
37C2×C3×Dic3⋊C4C2212yes—
38C2×#3724C2212yes—
39C2×Dic3⋊Dic3C2212yes—
40C2×Dic3⋊Dic3C2212yes—
41#63964C22116yescomplemented
42#63962C2218yescomplemented
43#63961C2218yescomplemented
44C2×(C2×D3)⋊Dic3C2212yes—
45C2×(C2×D3)⋊Dic3C2212yes—
46#63959C22116yescomplemented
47#63955C2218yescomplemented
48C2×Dic32C2212yes—
49#63851C22116yescomplemented
50#63839C22116yescomplemented
51C22×C3×#41—31no—
52C22×#237D311yescharacteristic
53C23×Dic6—31no—
54C23×Dic6—31no—
55C2×C3×#123—31no—
56#5825—316no—
57C2×#944—32no—
58C2×#936—32no—
59C2×#935—31no—
60C2×#935—31no—
61C2×#935—31no—
62C2×#935—31no—
63C2×#935—61no—
64C2×#935D311yescharacteristic, complemented
65C2×#929—31no—
66C2×#926—31no—
67C2×#924—32no—
68C2×#924—32no—
69#5648—316no—
70C2×#896—32no—
71C2×#888—32no—
72C2×#886—31no—
73C2×#885—32no—
74C2×#878—32no—
75C2×#877—31no—
76C24×C32C2311yescharacteristic
77C24×C32C2311yescharacteristic
78C23×C3×D3C2311yescharacteristic
79C2×C32×D4—24no—
80C2×C32×D4C2314yes—
81C22×C32×C4C2311yescharacteristic
82C22×C3⋊Dic3—24no—
83C22×C3⋊Dic3C2312yes—
84C22×C3⋊Dic3C2314yes—
85C22×C3⋊Dic3C2312yes—
86C2×C3×#67—24no—
87C2×C3×#67—24no—
88C2×C3×#67C2314yes—
89C2×C3×#67C2314yes—
90C22×C3×Dic3—24no—
91C22×C3×Dic3—24no—
92C22×C3×Dic3D418yes—
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2312yes—
95C22×C3×Dic3C2314yes—
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2314yes—
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2314yes—
101C3×#237—232no—
102C2×C3×C4×D3—24no—
103C2×C3×C4×D3C2314yes—
104C2×C3×Dic6—24no—
105C2×C3×Dic6C2314yes—
106C2×#627—28no—
107C2×#627—28no—
108C2×#627—232no—
109C2×#627C2318yes—
110C2×#627C2318yes—
111#3757C2314yes—
112#3757C2318yes—
113#3750C2318yes—
114C3×#217C2314yes—
115C3×#217C2318yes—
116C3×Dic3⋊C4C2318yes—
117#3724C2318yes—
118Dic3⋊Dic3C2318yes—
119Dic3⋊Dic3C2318yes—
120(C2×D3)⋊Dic3C2318yes—
121(C2×D3)⋊Dic3C2318yes—
122Dic32C2318yes—
123C2×#536—91noSylow
124C2×C3×#41—38no—
125C2×C3×#41—68no—
126C22×C3×Q8—31no—
127C22×C3×D4—21no—
128C22×C3×D4—31no—
129C22×C3×D4—31no—
130C22×C3×D4C2×D311yescharacteristic
131C22×C3×D4C2×D311yescharacteristic
132C23×C3×C4—31no—
133C23×C3×C4—31no—
134C23×C3×C4—31no—
135C23×C3×C4—31no—
136C22×#67C2×D311yescharacteristic
137C22×#67C2×D311yescharacteristic
138C23×Dic3—31no—
139C23×Dic3—31no—
140C23×Dic3—61no—
141C23×Dic3C2×D311yescharacteristic
142C23×Dic3C2×D311yescharacteristic
143C23×Dic3C2×D311yescharacteristic
144C2×#237—28no—
145C2×#237C2×D318yes—
146C22×C4×D3C2×D311yescharacteristic
147C22×Dic6—38no—
148C22×Dic6—32no—
149C22×Dic6—32no—
150C22×Dic6—32no—
151C22×Dic6—32no—
152C22×Dic6—38no—
153C22×Dic6—68no—
154C22×Dic6—68no—
155C22×Dic6C2×D311yescharacteristic
156C3×#123—38no—
157C2×C3×C4⋊C4—32no—
158C2×C3×C22⋊C4—31no—
159C2×C3×C22⋊C4—32no—
160C2×#217—31no—
161C2×#217—32no—
162C2×#217—32no—
163C2×#217—31no—
164C2×#217—32no—
165C2×#217—32no—
166C2×#217—61no—
167C2×#217—62no—
168C2×#217C2×D312yes—
169C2×#217C2×D311yescharacteristic
170#944—316no—
171#936—316no—
172#935—38no—
173#935—38no—
174#935—38no—
175#935—38no—
176#935—68no—
177#935C2×D318yescomplemented
178#929—38no—
179C2×(C2×D3)⋊C4—32no—
180C2×(C2×D3)⋊C4—32no—
181#926—38no—
182C2×C4⋊Dic3—32no—
183C2×C4⋊Dic3—32no—
184#924—316no—
185#924—316no—
186C2×Dic3⋊C4—32no—
187C2×Dic3⋊C4—32no—
188C2×Dic3⋊C4—32no—
189C2×Dic3⋊C4—32no—
190C2×Dic3⋊C4—32no—
191C2×Dic3⋊C4—32no—
192C2×Dic3⋊C4—62no—
193C2×Dic3⋊C4C2×D312yes—
194C2×C4×Dic3—32no—
195C2×C4×Dic3—32no—
196#896—316no—
197#888—316no—
198#886—38no—
199#885—316no—
200#878—316no—
201#877—38no—
202C23×C32—24no—
203C23×C32—22no—
204C23×C32—24no—
205C23×C32C2×D414yes—
206C23×C32C2412yes—
207C23×C32C2412yes—
208C23×C32C2411yescharacteristic
209C22×C3×D3—22no—
210C22×C3×D3—24no—
211C22×C3×D3C2412yes—
212C32×D4—28no—
213C2×C32×C4—22no—
214C2×C32×C4C2412yes—
215C2×C3⋊Dic3—28no—
216C2×C3⋊Dic3—24no—
217C2×C3⋊Dic3—24no—
218C2×C3⋊Dic3C2414yes—
219C2×C3⋊Dic3C2414yes—
220C3×#67—28no—
221C3×#67—28no—
222C2×C3×Dic3—28no—
223C2×C3×Dic3—24no—
224C2×C3×Dic3—22no—
225C2×C3×Dic3—24no—
226C2×C3×Dic3—28no—
227C2×C3×Dic3C2×D414yes—
228C2×C3×Dic3C2×D414yes—
229C2×C3×Dic3C2×D4116yes—
230C2×C3×Dic3C2414yes—
231C2×C3×Dic3C2414yes—
232C2×C3×Dic3C2412yes—
233C2×C3×Dic3C2412yes—
234C2×C3×Dic3C2412yes—
235C3×C4×D3—28no—
236C3×Dic6—28no—
237#627—216no—
238#627—216no—
239C22×#41—31no—
240C23×Q8—91no—
241#536—916no—
242C2×C4⋊Q8—92no—
243C2×#124—92no—
244C2×#123—31no—
245C2×#123—91no—
246C2×#123—91no—
247C2×#123—91no—
248C2×C22⋊Q8—92no—
249C2×C22⋊Q8—92no—
250C2×#117—91no—
251C24×C3—21no—
252C24×C3—21no—
253C24×C3—31no—
254C24×C3C22×D311yescharacteristic
255C24×C3C22×D311yescharacteristic
256C24×C3C22×D311yescharacteristic
257C24×C3C22×D311yescharacteristic
258C23×D3C22×D311yescharacteristic
259C3×#41—632no—
260C2×C3×Q8—34no—
261C2×C3×Q8—64no—
262C2×C3×D4—24no—
263C2×C3×D4—24no—
264C2×C3×D4—24no—
265C2×C3×D4—34no—
266C2×C3×D4—34no—
267C2×C3×D4—44no—
268C2×C3×D4—64no—
269C2×C3×D4—64no—
270C2×C3×D4C22×D314yes—
271C2×C3×D4C22×D314yes—
272C22×C3×C4—21no—
273C22×C3×C4—38no—
274C22×C3×C4—31no—
275C22×C3×C4—31no—
276C22×C3×C4—34no—
277C22×C3×C4—32no—
278C22×C3×C4—31no—
279C22×C3×C4—32no—
280C22×C3×C4—34no—
281C22×C3×C4—34no—
282C22×C3×C4—34no—
283C22×C3×C4—64no—
284C22×C3×C4—64no—
285C22×C3×C4—64no—
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C2×#67—24no—
289C2×#67—24no—
290C2×#67C22×D314yes—
291C2×#67C22×D314yes—
292C22×Dic3—24no—
293C22×Dic3—24no—
294C22×Dic3—34no—
295C22×Dic3—32no—
296C22×Dic3—32no—
297C22×Dic3—32no—
298C22×Dic3—32no—
299C22×Dic3—34no—
300C22×Dic3—62no—
301C22×Dic3—62no—
302C22×Dic3—64no—
303C22×Dic3—64no—
304C22×Dic3—64no—
305C22×Dic3—124no—
306C22×Dic3#6718yes—
307C22×Dic3C22×D314yes—
308C22×Dic3C22×D312yes—
309C22×Dic3C22×D311yescharacteristic
310C22×Dic3C22×D312yes—
311C22×Dic3C22×D314yes—
312C22×Dic3C22×D314yes—
313C22×Dic3C22×D311yescharacteristic
314C22×Dic3C22×D311yescharacteristic
315#237—232no—
316C2×C4×D3—24no—
317C2×C4×D3C22×D314yes—
318C2×Dic6—24no—
319C2×Dic6—38no—
320C2×Dic6—38no—
321C2×Dic6—38no—
322C2×Dic6—38no—
323C2×Dic6—68no—
324C2×Dic6—68no—
325C2×Dic6—632no—
326C2×Dic6—68no—
327C2×Dic6—68no—
328C2×Dic6—632no—
329C2×Dic6C22×D314yes—
330C3×C4⋊C4—38no—
331C3×C22⋊C4—34no—
332C3×C22⋊C4—38no—
333#217—34no—
334#217—38no—
335#217—38no—
336#217—34no—
337#217—38no—
338#217—38no—
339#217—64no—
340#217—68no—
341#217C22×D318yes—
342#217C22×D314yes—
343(C2×D3)⋊C4—38no—
344(C2×D3)⋊C4—38no—
345C4⋊Dic3—38no—
346C4⋊Dic3—38no—
347Dic3⋊C4—38no—
348Dic3⋊C4—38no—
349Dic3⋊C4—38no—
350Dic3⋊C4—38no—
351Dic3⋊C4—38no—
352Dic3⋊C4—38no—
353Dic3⋊C4—68no—
354Dic3⋊C4C22×D318yes—
355C4×Dic3—38no—
356C4×Dic3—38no—
357C22×C32—28no—
358C22×C32—24no—
359C22×C32—22no—
360C22×C32—24no—
361C22×C32—44no—
362C22×C32C22×D414yes—
363C22×C32C22×D412yes—
364C22×C322−1+414yes—
365C22×C32C2511yescharacteristic
366C2×C3×D3—22no—
367C2×C3×D3—24no—
368C2×C3×D3—44no—
369C32×C4—22no—
370C3⋊Dic3—24no—
371C3⋊Dic3—24no—
372C3×Dic3—24no—
373C3×Dic3—22no—
374C3×Dic3—24no—
375C3×Dic3C22×D414yes—
376C3×Dic3C22×D414yes—
377C2×#41—38no—
378C2×#41—68no—
379C22×Q8—31no—
380C22×Q8—92no—
381C22×Q8—92no—
382C22×Q8—98no—
383C22×Q8—188no—
384C22×D4—31no—
385C22×D4—31no—
386C22×D4D3211yescharacteristic
387C23×C4—31no—
388C23×C4—31no—
389C23×C4—31no—
390C23×C4—31no—
391C23×C4—91no—
392C4⋊Q8—916no—
393#124—916no—
394#123—38no—
395#123—98no—
396#123—98no—
397#123—98no—
398C22⋊Q8—916no—
399C22⋊Q8—916no—
400#117—98no—
401C2×C4⋊C4—32no—
402C2×C4⋊C4—92no—
403C2×C4⋊C4—92no—
404C2×C4⋊C4—92no—
405C2×C4⋊C4—92no—
406C2×C22⋊C4—31no—
407C2×C22⋊C4—32no—
408C2×C22⋊C4—92no—
409C2×C22⋊C4—92no—
410C2×C22⋊C4—91no—
411C2×C22⋊C4—92no—
412C2×C42—92no—
413C23×C3—24no—
414C23×C3—24no—
415C23×C3—22no—
416C23×C3—24no—
417C23×C3—24no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—21no—
422C23×C3—24no—
423C23×C3—32no—
424C23×C3—44no—
425C23×C3—42no—
426C23×C3—44no—
427C23×C3—62no—
428C23×C3—64no—
429C23×C3D3×D414yes—
430C23×C3C2×#6714yes—
431C23×C3C23×D312yes—
432C23×C3C23×D312yes—
433C23×C3C23×D312yes—
434C23×C3C23×D312yes—
435C23×C3C23×D311yescharacteristic
436C23×C3C23×D311yescharacteristic
437C22×D3—24no—
438C22×D3—22no—
439C22×D3C23×D312yes—
440C3×Q8—68no—
441C3×D4—28no—
442C3×D4—28no—
443C3×D4—48no—
444C3×D4—68no—
445C3×D4—68no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—34no—
450C2×C3×C4—34no—
451C2×C3×C4—316no—
452C2×C3×C4—32no—
453C2×C3×C4—32no—
454C2×C3×C4—34no—
455C2×C3×C4—32no—
456C2×C3×C4—34no—
457C2×C3×C4—42no—
458C2×C3×C4—68no—
459C2×C3×C4—68no—
460C2×C3×C4—62no—
461C2×C3×C4—64no—
462C2×C3×C4—68no—
463C2×C3×C4—64no—
464C2×C3×C4C23×D312yes—
465C2×C3×C4C23×D312yes—
466#67—28no—
467#67—28no—
468C2×Dic3—28no—
469C2×Dic3—24no—
470C2×Dic3—24no—
471C2×Dic3—22no—
472C2×Dic3—28no—
473C2×Dic3—34no—
474C2×Dic3—34no—
475C2×Dic3—34no—
476C2×Dic3—34no—
477C2×Dic3—64no—
478C2×Dic3—64no—
479C2×Dic3—68no—
480C2×Dic3—64no—
481C2×Dic3—64no—
482C2×Dic3—64no—
483C2×Dic3—68no—
484C2×Dic3—64no—
485C2×Dic3—124no—
486C2×Dic3—124no—
487C2×Dic3—128no—
488C2×Dic3C2×#6714yes—
489C2×Dic3C2×#6714yes—
490C2×Dic3C2×#67116yes—
491C2×Dic3C23×D314yes—
492C2×Dic3C23×D312yes—
493C2×Dic3C23×D314yes—
494C2×Dic3C23×D312yes—
495C2×Dic3C23×D312yes—
496C4×D3—28no—
497Dic6—28no—
498Dic6—616no—
499Dic6—616no—
500Dic6—616no—
501Dic6—616no—
502C2×C32—24no—
503C2×C32—42no—
504C2×C32#53614yescomplemented
505C2×C32C23×D411yescharacteristic
506C2×C32C2×2−1+412yes—
507C3×D3—42no—
508C24—31no—
509C24C2×D3211yescharacteristic
510C24C2×D3211yescharacteristic
511#41—632no—
512C2×Q8—34no—
513C2×Q8—64no—
514C2×Q8—98no—
515C2×Q8—98no—
516C2×Q8—188no—
517C2×Q8—188no—
518C2×Q8—1832no—
519C2×D4—24no—
520C2×D4—34no—
521C2×D4—34no—
522C2×D4—64no—
523C2×D4—64no—
524C2×D4C2×D3214yes—
525C22×C4—34no—
526C22×C4—31no—
527C22×C4—31no—
528C22×C4—38no—
529C22×C4—34no—
530C22×C4—34no—
531C22×C4—32no—
532C22×C4—32no—
533C22×C4—31no—
534C22×C4—34no—
535C22×C4—64no—
536C22×C4—64no—
537C22×C4—64no—
538C22×C4—94no—
539C22×C4—92no—
540C22×C4—92no—
541C22×C4—184no—
542C22×C4C2×D3211yescharacteristic
543C4⋊C4—38no—
544C4⋊C4—98no—
545C4⋊C4—98no—
546C4⋊C4—98no—
547C4⋊C4—98no—
548C22⋊C4—34no—
549C22⋊C4—38no—
550C22⋊C4—98no—
551C22⋊C4—98no—
552C22⋊C4—94no—
553C22⋊C4—98no—
554C42—98no—
555C22×C3—28no—
556C22×C3—24no—
557C22×C3—24no—
558C22×C3—28no—
559C22×C3—22no—
560C22×C3—24no—
561C22×C3—24no—
562C22×C3—22no—
563C22×C3—24no—
564C22×C3—22no—
565C22×C3—24no—
566C22×C3—21no—
567C22×C3—44no—
568C22×C3—48no—
569C22×C3—42no—
570C22×C3—44no—
571C22×C3—44no—
572C22×C3—44no—
573C22×C3—62no—
574C22×C3—64no—
575C22×C3—84no—
576C22×C3—124no—
577C22×C3C2×D3×D414yes—
578C22×C3C2×D3×D412yes—
579C22×C3#101014yes—
580C22×C3#101014yes—
581C22×C3C22×#6714yes—
582C22×C3C22×#6712yes—
583C22×C3C24×D311yescharacteristic
584C22×C3C24×D311yescharacteristic
585C2×D3—24no—
586C2×D3—22no—
587C2×D3—44no—
588C3×C4—22no—
589C3×C4—22no—
590C3×C4—34no—
591C3×C4—34no—
592C3×C4—42no—
593C3×C4—62no—
594C3×C4—64no—
595C3×C4—64no—
596Dic3—24no—
597Dic3—24no—
598Dic3—22no—
599Dic3—64no—
600Dic3—64no—
601Dic3—64no—
602Dic3—64no—
603Dic3—124no—
604Dic3—124no—
605Dic3C22×#6714yes—
606Dic3C22×#6714yes—
607C32C2×#53611yescharacteristic, complemented, Sylow
608C23—24no—
609C23—24no—
610C23—22no—
611C23—32no—
612C23—64no—
613C23—62no—
614C23D3×#6714yes—
615C23C22×D3212yes—
616C23C22×D3212yes—
617C23C22×D3211yescharacteristic
618Q8—68no—
619Q8—1816no—
620Q8—1816no—
621D4—28no—
622D4—68no—
623D4—68no—
624C2×C4—22no—
625C2×C4—34no—
626C2×C4—34no—
627C2×C4—316no—
628C2×C4—32no—
629C2×C4—32no—
630C2×C4—34no—
631C2×C4—34no—
632C2×C4—32no—
633C2×C4—68no—
634C2×C4—68no—
635C2×C4—64no—
636C2×C4—62no—
637C2×C4—68no—
638C2×C4—64no—
639C2×C4—94no—
640C2×C4—94no—
641C2×C4—184no—
642C2×C4—188no—
643C2×C4—184no—
644C2×C4C22×D3212yes—
645C2×C3—24no—
646C2×C3—24no—
647C2×C3—22no—
648C2×C3—21no—
649C2×C3—24no—
650C2×C3—44no—
651C2×C3—42no—
652C2×C3—42no—
653C2×C3—82no—
654C2×C3—122no—
655C2×C3#564814yescomplemented
656C2×C3#582514yescomplemented
657C2×C3C22×D3×D411yescharacteristic
658C2×C3C2×#101012yes—
659C2×C3C2×#101012yes—
660C2×C3C23×#6711yescharacteristic
661D3—42no—
662C22—24no—
663C22—28no—
664C22—24no—
665C22—22no—
666C22—44no—
667C22—64no—
668C22—62no—
669C22—124no—
670C22#6430914yes—
671C22C2×D3×#6714yes—
672C22C2×D3×#6712yes—
673C22C23×D3211yescharacteristic
674C4—22no—
675C4—34no—
676C4—34no—
677C4—64no—
678C4—62no—
679C4—64no—
680C4—184no—
681C4—184no—
682C3—21no—
683C3C2×#564811yescharacteristic, complemented
684C3C2×#582511yescharacteristic, complemented
685C2—24no—
686C2—42no—
687C2—122no—
688C2#1059527014yesdirect product factor
689C2C2×#6430912yes—
690C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
prime radicalC22×C3×#237C2
hypercenterC22×D4D32
hypocenterC32C2×#536
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C23×#627C2semidirect
3. C2×#64144C2semidirect
4. C2×C3×#935C2semidirect
5. C2×#63964C2semidirect
6. C2×#63962C2semidirect
7. C2×#63961C2semidirect
8. C2×#63959C2semidirect
9. C2×#63955C2semidirect
10. #10595270C2direct (N × H)
11. C2×#63851C2semidirect
12. C2×#63839C2semidirect
29. C22×#627C22semidirect
32. #64144C22semidirect
36. C3×#935C22semidirect
41. #63964C22semidirect
42. #63962C22semidirect
43. #63961C22semidirect
46. #63959C22semidirect
47. #63955C22semidirect
49. #63851C22semidirect
50. #63839C22semidirect
64. C2×#935D3semidirect
177. #935C2×D3semidirect
504. C2×C32#536semidirect
607. C32C2×#536semidirect
655. C2×C3#5648semidirect
656. C2×C3#5825semidirect
683. C3C2×#5648semidirect
684. C3C2×#5825semidirect
688. C2#10595270direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C23×#6272
C2×#641442
C2×C3×#9352
C2×#639642
C2×#639622
C2×#639612
C2×#639592
C2×#639552
#105952702
C2×#638512
C2×#638392
C2×#58253
C2×#56483