Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
250 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 30 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 | #66359⋊C2 |
| commutator, cosocle, hypocenter | #66359 | C2×C3 |
| Frattini | C32 | C3×C3⋊S4 |
| Fitting | C22×C32×C9 | D3 |
| socle | C22×C32 | #272 |
| LCS | G ▷ #66359 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#66359 | C2 | semidirect |
| 4. #66359⋊C2 | C3 | direct (N × H) |
| 12. #66359 | C2×C3 | semidirect |
| 122. C22×C3 | #733⋊C2 | semidirect |
| 151. C22 | C3×#733⋊C2 | semidirect |
| 156. C3 | #66359⋊C2 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66359 | 2 |
| C3×((C22⋊C9)⋊C2)⋊C3 | 3 |
| C32×#611 | 3 |
| #66359⋊C2 | 3 |
| C3×#733⋊C2 | 4 |