Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
476 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 23 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 | #10619775 |
| commutator, hypocenter | C22×C33 | C2×C9 |
| Frattini | C33 | D3×A4 |
| Fitting, cosocle | C22×C34 | C2×C3 |
| socle | C22×C32 | (C3⋊D3)⋊C3 |
| prime radical | C22×C3×C3⋊(C3⋊D3) | C3 |
| LCS | G ▷ C22×C33 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11757461 | C2 | semidirect |
| 9. C32⋊(C22⋊C9) | D3 | semidirect |
| 11. C22×C3⋊(C3⋊D3) | C9 | semidirect |
| 25. C22×C33 | C2×C9 | semidirect |
| 55. C3⋊(C3⋊D3) | C22⋊C9 | semidirect |
| 95. C33 | C2×C22⋊C9 | semidirect |
| 177. C22 | #92173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757461 | 2 |
| C22×C3×C3⋊(C3⋊D3) | 3 |
| (C3⋊D3)⋊(C22⋊C9) | 3 |
| #92173 | 4 |