Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
204 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #10620070 |
| commutator, Fitting, cosocle, hypocenter | C22×C32⋊C9 | C2×C3 |
| Frattini | C32 | A4×C3⋊D3 |
| socle | C22×C32 | C3×C3⋊D3 |
| prime radical | C22×#4181 | C3 |
| LCS | G ▷ C22×C32⋊C9 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11757769 | C2 | semidirect |
| 12. C9⋊(C22⋊C9) | D3 | semidirect |
| 15. C9×C22⋊C9 | D3 | semidirect |
| 145. C22 | #92308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757769 | 2 |
| C22×#4181 | 3 |
| (C3⋊D3)⋊(C22⋊C9) | 3 |
| D9×C22⋊C9 | 3 |
| D9⋊(C22⋊C9) | 3 |
| #92308 | 4 |