Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
196 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×Dic3×C27 | C2 | semidirect |
| 6. C3⋊D3×C27 | C4 | semidirect |
| 13. Dic3×C27 | D3 | semidirect |
| 14. C32×C27 | C2×C4 | semidirect |
| 40. C3×C27 | C4×D3 | semidirect |
| 42. #624 | C27 | direct (N × H) |
| 61. C3×Dic3 | C2×C27 | semidirect |
| 73. C27 | #624 | direct (N × H) |
| 81. C3⋊D3 | C4×C27 | semidirect |
| 94. Dic3 | D3×C27 | semidirect |
| 98. C32 | C2×C4×C27 | semidirect |
| 117. C3 | C4×D3×C27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊D3×C27 | 2 |
| C3×Dic3×C27 | 2 |
| C9×#624 | 3 |
| C4×D3×C27 | 3 |