Subgroups — C₃×C₄×C₄₃₃⋊C₃ #29510294

Order 15588.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄₃₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄₃₃⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₄×C₄₃₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄₃₃⋊C₃	C₄	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₃×C₄₃₃	C₂×C₃	1	1	yes	characteristic
6	C₂×C₄₃₃⋊C₃	C₂×C₃	1	3	yes	—
7	C₄×C₄₃₃	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₄₃₃	C₃×C₄	1	1	yes	characteristic, complemented
9	C₄₃₃⋊C₃	C₃×C₄	1	3	yes	direct product factor
10	C₂×C₄₃₃	C₂×C₃²	1	1	yes	characteristic
11	C₄₃₃	C₃²×C₄	1	1	yes	characteristic, complemented, Sylow
12	C₃²×C₄	—	433	1	no	maximal, Hall
13	C₂×C₃²	—	433	1	no	—
14	C₃×C₄	—	433	3	no	—
15	C₃×C₄	C₄₃₃⋊C₃	1	1	yes	characteristic, direct product factor
16	C₃²	—	433	1	no	Sylow
17	C₂×C₃	—	433	3	no	—
18	C₂×C₃	C₂×C₄₃₃⋊C₃	1	1	yes	characteristic
19	C₄	C₃×C₄₃₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₃	—	433	3	no	—
21	C₃	C₄×C₄₃₃⋊C₃	1	1	yes	characteristic, direct product factor
22	C₂	C₂×C₃×C₄₃₃⋊C₃	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.