Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
249 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 249 conjugacy classes of subgroups — too many to draw. Only its 62 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. C32×#349 | C2 | semidirect |
| 3. C3×C3⋊#338 | C2 | semidirect |
| 5. #67535 | C3 | direct (N × H) |
| 16. C3×#349 | D3 | semidirect |
| 17. C3×#349 | C2×C3 | semidirect |
| 19. C3⋊#338 | C2×C3 | semidirect |
| 64. #349 | C3×D3 | semidirect |
| 190. C32 | #1341 | semidirect |
| 226. C3 | #67535 | direct (N × H) |
| 227. C3 | C3×#1341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5135 | 2 |
| C32×#349 | 2 |
| C3×C3⋊#338 | 2 |
| C3×#1341 | 3 |
| #67535 | 3 |