Subgroups — #37559262

Order 23872.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₉₈₄	C₂	1	1	yes	maximal, characteristic
2	#26045698	C₂	1	1	yes	maximal, characteristic
3	Q₃₂×C₃₇₃	C₂	1	1	yes	maximal, characteristic
4	Dic₁₄₉₂	—	2	1	no	—
5	Q₁₆×C₃₇₃	—	2	1	no	—
6	C₁₆×C₃₇₃	C₂²	1	1	yes	characteristic
7	Dic₇₄₆	—	4	1	no	—
8	Q₈×C₃₇₃	—	4	1	no	—
9	C₈×C₃₇₃	D₄	1	1	yes	characteristic
10	C₄×C₃₇₃	—	8	1	no	—
11	C₄×C₃₇₃	D₈	1	1	yes	characteristic
12	Dic₃₇₃	—	8	1	no	—
13	C₂×C₃₇₃	D₁₆	1	1	yes	characteristic
14	C₃₇₃	Q₆₄	1	1	yes	characteristic, complemented, Sylow
15	Q₆₄	—	373	1	no	maximal, Sylow
16	Q₃₂	—	373	1	no	—
17	Q₃₂	D₃₇₃	1	1	yes	characteristic
18	C₃₂	—	373	1	no	—
19	Q₁₆	—	2	1	no	—
20	Q₁₆	—	746	1	no	—
21	C₁₆	C₂×D₃₇₃	1	1	yes	characteristic
22	Q₈	—	4	1	no	—
23	Q₈	—	1492	1	no	—
24	C₈	C₂²⋊D₃₇₃	1	1	yes	characteristic
25	C₄	—	8	1	no	—
26	C₄	—	2984	1	no	—
27	C₄	#20238595	1	1	yes	characteristic
28	C₂	#26045733	1	1	yes	characteristic

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

N	H ≅ G/N	type
14. C₃₇₃	Q₆₄	semidirect

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