Subgroups — #32973896

Order 18688.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₆₇₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#22607750	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×D₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	D₂₃₃₆	—	2	1	no	—
5	D₃₂×C₇₃	—	2	1	no	—
6	C₆₄×C₇₃	C₂²	1	1	yes	characteristic
7	D₁₁₆₈	—	4	1	no	—
8	D₁₆×C₇₃	—	4	1	no	—
9	C₃₂×C₇₃	D₄	1	1	yes	characteristic
10	D₅₈₄	—	8	1	no	—
11	D₈×C₇₃	—	8	1	no	—
12	C₁₆×C₇₃	D₈	1	1	yes	characteristic
13	D₄×C₇₃	—	16	1	no	—
14	D₂₉₂	—	16	1	no	—
15	C₈×C₇₃	D₁₆	1	1	yes	characteristic
16	C₂²×C₇₃	—	32	1	no	—
17	C₂×D₇₃	—	32	1	no	—
18	C₄×C₇₃	D₃₂	1	1	yes	characteristic
19	D₁₂₈	—	73	1	no	maximal, Sylow
20	C₂×C₇₃	—	64	1	no	—
21	C₂×C₇₃	D₆₄	1	1	yes	characteristic
22	D₇₃	—	64	1	no	—
23	D₆₄	—	73	1	no	—
24	D₆₄	D₇₃	1	1	yes	characteristic, complemented
25	C₁₂₈	—	73	1	no	—
26	C₇₃	D₁₂₈	1	1	yes	characteristic, complemented, Sylow
27	D₃₂	—	2	1	no	—
28	D₃₂	—	146	1	no	—
29	C₆₄	C₂×D₇₃	1	1	yes	characteristic
30	D₁₆	—	4	1	no	—
31	D₁₆	—	292	1	no	—
32	C₃₂	C₂²⋊D₇₃	1	1	yes	characteristic
33	D₈	—	8	1	no	—
34	D₈	—	584	1	no	—
35	C₁₆	#11924013	1	1	yes	characteristic
36	D₄	—	16	1	no	—
37	D₄	—	1168	1	no	—
38	C₈	#14556532	1	1	yes	characteristic
39	C₂²	—	32	1	no	—
40	C₂²	—	2336	1	no	—
41	C₄	#17988422	1	1	yes	characteristic
42	C₂	—	64	1	no	—
43	C₂	—	4672	1	no	—
44	C₂	#22608143	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.