Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
438 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 113 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. #10592895 | C2 | semidirect |
| 3. #10592594 | C2 | semidirect |
| 4. C32×#359 | C2 | semidirect |
| 5. #10589376 | C2 | semidirect |
| 6. C16×C3⋊Dic3 | C2 | semidirect |
| 7. #10589359 | C2 | semidirect |
| 16. #63656 | C4 | semidirect |
| 17. #63655 | C4 | semidirect |
| 18. #63654 | C4 | semidirect |
| 19. #63653 | C4 | semidirect |
| 27. C3×#359 | D3 | semidirect |
| 88. #359 | C3⋊D3 | semidirect |
| 181. C32 | #2178 | semidirect |
| 210. C3 | #69238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592895 | 2 |
| #10592893 | 2 |
| #10592594 | 2 |
| C32×#359 | 2 |
| #10589376 | 2 |
| C16×C3⋊Dic3 | 2 |
| #10589359 | 2 |
| #69238 | 3 |