Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
309 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 309 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 1. C3×#4878 | C2 | semidirect |
| 4. C3×#4492 | C2 | semidirect |
| 5. #10589117 | C2 | semidirect |
| 7. Dic3×C3⋊C16 | C2 | semidirect |
| 23. #4878 | D3 | semidirect |
| 30. #4492 | D3 | semidirect |
| 251. C32 | #2242 | semidirect |
| 290. C3 | #69216 | semidirect |
| 291. C3 | #71351 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4878 | 2 |
| #10590865 | 2 |
| #10589357 | 2 |
| C3×#4492 | 2 |
| #10589117 | 2 |
| #10589116 | 2 |
| Dic3×C3⋊C16 | 2 |
| #71351 | 3 |
| #69216 | 3 |