Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
303 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 303 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×#66359 | C2 |
| Frattini | C32 | C3⋊(C3⋊S4) |
| Fitting | C22×C32×C9 | D3 |
| socle | C22×C32 | #272 |
| LCS | G ▷ C3×#66359 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#66359 | C2 | semidirect |
| 10. #66359 | D3 | semidirect |
| 91. C22×C3 | #733⋊C2 | semidirect |
| 114. C22 | C3⋊(#733⋊C2) | semidirect |
| 118. C3 | #66359⋊C2 | semidirect |
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 |
| C3×#6233 | 3 |
| #66359⋊C2 | 3 |
| C3⋊(#733⋊C2) | 4 |