Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
315 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 315 conjugacy classes of subgroups — too many to draw. Only its 88 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. #10590919 | C2 | semidirect |
| 3. #10589368 | C2 | semidirect |
| 4. C3×#4506 | C2 | semidirect |
| 5. #10589120 | C2 | semidirect |
| 14. C3×Dic24 | C4 | semidirect |
| 15. C3×#800 | C4 | semidirect |
| 16. C3×D48 | C4 | semidirect |
| 24. #4506 | D3 | semidirect |
| 63. Dic24 | Dic3 | semidirect |
| 64. #800 | Dic3 | semidirect |
| 65. D48 | Dic3 | semidirect |
| 186. C32 | #2179 | semidirect |
| 212. C3 | #69358 | semidirect |
| 213. C3 | #71512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4904 | 2 |
| #10590919 | 2 |
| #10589368 | 2 |
| C3×#4506 | 2 |
| #10589120 | 2 |
| #71512 | 3 |
| #69358 | 3 |