Subgroups — #37559261

Order 23872.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₉₈₄	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅₉₆₈	C₂	1	1	yes	maximal, characteristic
3	C₃₂×C₃₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₁₄₉₂	—	2	1	no	—
5	D₂₉₈₄	—	2	1	no	—
6	C₁₆×C₃₇₃	C₂²	1	1	yes	characteristic
7	Dic₇₄₆	—	4	1	no	—
8	D₁₄₉₂	—	4	1	no	—
9	C₈×C₃₇₃	D₄	1	1	yes	characteristic
10	C₂×D₃₇₃	—	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	D₃₇₃	—	16	1	no	—
15	C₃₇₃	SD₆₄	1	1	yes	characteristic, complemented, Sylow
16	SD₆₄	—	373	1	no	maximal, Sylow
17	Q₃₂	—	373	1	no	—
18	D₁₆	—	373	1	no	—
19	C₃₂	D₃₇₃	1	1	yes	characteristic, complemented
20	Q₁₆	—	746	1	no	—
21	D₈	—	746	1	no	—
22	C₁₆	C₂×D₃₇₃	1	1	yes	characteristic
23	Q₈	—	1492	1	no	—
24	D₄	—	1492	1	no	—
25	C₈	D₁₄₉₂	1	1	yes	characteristic
26	C₂²	—	2984	1	no	—
27	C₄	—	2984	1	no	—
28	C₄	D₂₉₈₄	1	1	yes	characteristic
29	C₂	—	5968	1	no	—
30	C₂	D₅₉₆₈	1	1	yes	characteristic

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

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