Subgroups — #817

Order 96.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₃	C₂	1	2	yes	maximal
3	#106	—	3	1	no	maximal, Sylow
4	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
5	C₂×Dic₃	—	2	2	no	—
6	C₃×C₈	C₄	1	2	yes	complemented
7	C₂×C₈	D₃	1	1	yes	characteristic
8	C₄⋊C₄	—	3	2	no	—
9	C₂²×C₃	D₄	1	1	yes	characteristic
10	C₃×C₄	C₂×C₄	1	1	yes	characteristic
11	C₃×C₄	Q₈	1	1	yes	characteristic
12	Dic₃	—	4	2	no	—
13	C₂×C₄	—	6	2	no	—
14	C₂×C₄	C₂×D₃	1	1	yes	characteristic
15	C₈	Dic₃	1	2	yes	complemented
16	C₂×C₃	C₄⋊C₄	1	1	yes	characteristic
17	C₂×C₃	SD₁₆	1	2	yes	—
18	C₂²	D₁₂	1	1	yes	characteristic
19	C₄	—	12	2	no	—
20	C₄	Dic₆	1	1	yes	characteristic
21	C₄	C₂×Dic₃	1	1	yes	characteristic
22	C₃	#106	1	1	yes	characteristic, complemented, Sylow
23	C₂	#204	1	2	yes	—
24	C₂	C₄⋊Dic₃	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.