Subgroups — #803

Order 96.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊C₈	C₂	1	2	yes	maximal
3	#97	—	3	1	no	maximal, Sylow
4	C₂×C₃×C₄	C₄	1	2	yes	—
5	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
6	C₃⋊C₈	C₄	1	4	yes	complemented
7	C₂×C₈	—	3	2	no	—
8	C₄²	D₃	1	1	yes	characteristic
9	C₂²×C₃	C₂×C₄	1	1	yes	characteristic
10	C₃×C₄	—	2	2	no	—
11	C₃×C₄	C₂×C₄	1	2	yes	—
12	C₂×C₄	Dic₃	1	2	yes	—
13	C₂×C₄	C₂×D₃	1	1	yes	characteristic
14	C₈	—	3	4	no	—
15	C₂×C₃	C₄²	1	1	yes	characteristic
16	C₂×C₃	M₁₆	1	2	yes	—
17	C₂²	C₂×Dic₃	1	1	yes	characteristic
18	C₄	—	2	2	no	—
19	C₄	C₄×D₃	1	2	yes	—
20	C₃	#97	1	1	yes	characteristic, complemented, Sylow
21	C₂	#208	1	2	yes	—
22	C₂	C₄×Dic₃	1	1	yes	characteristic

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

N	H ≅ G/N	type
6. C₃⋊C₈	C₄	semidirect
20. C₃	#97	semidirect

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