Subgroups — #32973901

Order 18688.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₃₃₆	C₂	1	1	yes	maximal, characteristic
2	#22607750	C₂	1	1	yes	maximal, characteristic
3	C₇₃×Q₁₂₈	C₂	1	1	yes	maximal, characteristic
4	Dic₁₁₆₈	—	2	1	no	—
5	Q₆₄×C₇₃	—	2	1	no	—
6	C₆₄×C₇₃	C₂²	1	1	yes	characteristic
7	Dic₅₈₄	—	4	1	no	—
8	Q₃₂×C₇₃	—	4	1	no	—
9	C₃₂×C₇₃	D₄	1	1	yes	characteristic
10	Dic₂₉₂	—	8	1	no	—
11	Q₁₆×C₇₃	—	8	1	no	—
12	C₁₆×C₇₃	D₈	1	1	yes	characteristic
13	Q₈×C₇₃	—	16	1	no	—
14	Dic₁₄₆	—	16	1	no	—
15	C₈×C₇₃	D₁₆	1	1	yes	characteristic
16	C₄×C₇₃	—	32	1	no	—
17	C₄×C₇₃	D₃₂	1	1	yes	characteristic
18	Dic₇₃	—	32	1	no	—
19	Q₂₅₆	—	73	1	no	maximal, Sylow
20	C₂×C₇₃	D₆₄	1	1	yes	characteristic
21	Q₁₂₈	—	73	1	no	—
22	Q₁₂₈	D₇₃	1	1	yes	characteristic
23	C₁₂₈	—	73	1	no	—
24	C₇₃	Q₂₅₆	1	1	yes	characteristic, complemented, Sylow
25	Q₆₄	—	2	1	no	—
26	Q₆₄	—	146	1	no	—
27	C₆₄	C₂×D₇₃	1	1	yes	characteristic
28	Q₃₂	—	4	1	no	—
29	Q₃₂	—	292	1	no	—
30	C₃₂	C₂²⋊D₇₃	1	1	yes	characteristic
31	Q₁₆	—	8	1	no	—
32	Q₁₆	—	584	1	no	—
33	C₁₆	#11924013	1	1	yes	characteristic
34	Q₈	—	16	1	no	—
35	Q₈	—	1168	1	no	—
36	C₈	#14556532	1	1	yes	characteristic
37	C₄	—	32	1	no	—
38	C₄	—	2336	1	no	—
39	C₄	#17988422	1	1	yes	characteristic
40	C₂	#22608143	1	1	yes	characteristic

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

N	H ≅ G/N	type
24. C₇₃	Q₂₅₆	semidirect

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