Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
666 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 666 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 3. #10592818 | C2 | semidirect |
| 5. C2×#63642 | C2 | semidirect |
| 6. C32×#341 | C2 | semidirect |
| 7. #10589421 | C2 | semidirect |
| 17. #63648 | C4 | semidirect |
| 19. #63643 | C4 | semidirect |
| 27. C3×#341 | D3 | semidirect |
| 99. #341 | C3⋊D3 | semidirect |
| 223. C32 | #1938 | semidirect |
| 266. C3 | #68919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63652 | 2 |
| #10592828 | 2 |
| #10592818 | 2 |
| #10592812 | 2 |
| C2×#63642 | 2 |
| C32×#341 | 2 |
| #10589421 | 2 |
| #68919 | 3 |