Subgroups — C₄×3₋¹⁺² #1087

Order 108.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₄	C₃	1	1	yes	maximal, characteristic
3	C₄×C₉	C₃	1	3	yes	maximal, complemented
4	3₋¹⁺²	C₄	1	1	yes	characteristic, direct product factor, Sylow
5	C₂×C₃²	C₂×C₃	1	1	yes	characteristic
6	C₂×C₉	C₂×C₃	1	3	yes	—
7	C₃×C₄	—	3	1	no	—
8	C₃×C₄	C₃²	1	1	yes	characteristic
9	C₃²	C₃×C₄	1	1	yes	characteristic
10	C₉	C₃×C₄	1	3	yes	complemented
11	C₂×C₃	—	3	1	no	—
12	C₂×C₃	C₂×C₃²	1	1	yes	characteristic
13	C₄	3₋¹⁺²	1	1	yes	characteristic, direct product factor, Sylow
14	C₃	—	3	1	no	—
15	C₃	C₃²×C₄	1	1	yes	characteristic
16	C₂	C₂×3₋¹⁺²	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.