Subgroups — C₃×#107 #850

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	C₃×C₄⋊C₄	C₂	1	2	yes	maximal
3	#107	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×C₄	—	2	2	no	—
5	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
6	C₃×C₈	C₄	1	2	yes	complemented
7	C₂×C₈	C₂×C₃	1	1	yes	characteristic
8	C₄⋊C₄	C₂×C₃	1	2	yes	—
9	C₂²×C₃	D₄	1	1	yes	characteristic
10	C₃×C₄	—	4	2	no	—
11	C₃×C₄	C₂×C₄	1	1	yes	characteristic
12	C₃×C₄	Q₈	1	1	yes	characteristic
13	C₂×C₄	—	2	2	no	—
14	C₂×C₄	C₂²×C₃	1	1	yes	characteristic
15	C₈	C₃×C₄	1	2	yes	complemented
16	C₂×C₃	C₄⋊C₄	1	1	yes	characteristic
17	C₂×C₃	D₈	1	1	yes	characteristic
18	C₂×C₃	Q₁₆	1	1	yes	characteristic
19	C₂²	C₃×D₄	1	1	yes	characteristic
20	C₄	—	4	2	no	—
21	C₄	C₂×C₃×C₄	1	1	yes	characteristic
22	C₄	C₃×Q₈	1	1	yes	characteristic
23	C₃	#107	1	1	yes	characteristic, direct product factor, Sylow
24	C₂	C₃×C₄⋊C₄	1	1	yes	characteristic
25	C₂	C₃×D₈	1	1	yes	characteristic
26	C₂	C₃×Q₁₆	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.