Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
421 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 421 conjugacy classes of subgroups — too many to draw. Only its 68 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. #10592850 | C2 | semidirect |
| 2. C3×#5147 | C2 | semidirect |
| 3. #10590919 | C2 | semidirect |
| 4. #10590634 | C2 | semidirect |
| 5. C3×#4563 | C2 | semidirect |
| 6. #10589135 | C2 | semidirect |
| 7. #10589128 | C2 | semidirect |
| 31. #5147 | D3 | semidirect |
| 35. #4563 | D3 | semidirect |
| 54. C3×Dic12 | D4 | semidirect |
| 55. C3×D24 | D4 | semidirect |
| 161. Dic12 | #67 | semidirect |
| 168. D24 | #67 | semidirect |
| 304. C32 | #2213 | semidirect |
| 348. C3 | #69263 | semidirect |
| 349. C3 | #71514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592850 | 2 |
| C3×#5147 | 2 |
| #10590919 | 2 |
| #10590634 | 2 |
| C3×#4563 | 2 |
| #10589135 | 2 |
| #10589128 | 2 |
| #71514 | 3 |
| #69263 | 3 |