Subgroups — #829

Order 96.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	Dic₁₂	C₂	1	1	yes	maximal, characteristic
3	C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	Q₃₂	—	3	1	no	maximal, Sylow
5	C₃×Q₈	—	2	1	no	—
6	Dic₆	—	2	1	no	—
7	C₃×C₈	C₂²	1	1	yes	characteristic
8	Q₁₆	—	3	1	no	—
9	Q₁₆	D₃	1	1	yes	characteristic
10	C₁₆	—	3	1	no	—
11	C₃×C₄	—	4	1	no	—
12	C₃×C₄	D₄	1	1	yes	characteristic
13	Dic₃	—	4	1	no	—
14	Q₈	—	2	1	no	—
15	Q₈	—	6	1	no	—
16	C₈	C₂×D₃	1	1	yes	characteristic
17	C₂×C₃	D₈	1	1	yes	characteristic
18	C₄	—	4	1	no	—
19	C₄	—	12	1	no	—
20	C₄	#67	1	1	yes	characteristic
21	C₃	Q₃₂	1	1	yes	characteristic, complemented, Sylow
22	C₂	#213	1	1	yes	characteristic

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

N	H ≅ G/N	type
21. C₃	Q₃₂	semidirect

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