Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
243 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 243 conjugacy classes of subgroups — too many to draw. Only its 78 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. #10589323 | C2 | semidirect |
| 3. C3×#4461 | C2 | semidirect |
| 16. #4461 | D3 | semidirect |
| 29. C3×D24 | C8 | semidirect |
| 86. D24 | C3⋊C8 | semidirect |
| 174. C32 | #1333 | semidirect |
| 208. C3 | #67516 | semidirect |
| 209. C3 | #67762 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D24 | 2 |
| #10589323 | 2 |
| C3×#4461 | 2 |
| #67762 | 3 |
| #67516 | 3 |