Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
334 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 84 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. #10590917 | C2 | semidirect |
| 3. C3×#4506 | C2 | semidirect |
| 4. C3×Dic3×C16 | C2 | semidirect |
| 5. #10589122 | C2 | semidirect |
| 11. #63628 | C4 | semidirect |
| 12. #63627 | C4 | semidirect |
| 13. #63626 | C4 | semidirect |
| 26. #4506 | D3 | semidirect |
| 27. Dic3×C16 | D3 | semidirect |
| 195. C32 | #2178 | semidirect |
| 223. C3 | #69067 | semidirect |
| 224. C3 | #69357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592603 | 2 |
| #10590917 | 2 |
| C3×#4506 | 2 |
| C3×Dic3×C16 | 2 |
| #10589122 | 2 |
| #69357 | 3 |
| #69067 | 3 |