Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
690 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 193 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. C2×C32×C4×C8 | C2 | semidirect |
| 4. #10592801 | C2 | semidirect |
| 6. #10589418 | C2 | semidirect |
| 7. #10589389 | C2 | semidirect |
| 17. #63648 | C4 | semidirect |
| 19. #63643 | C4 | semidirect |
| 22. C2×C3×C4×C8 | D3 | semidirect |
| 98. C2×C4×C8 | C3⋊D3 | semidirect |
| 223. C32 | #1937 | semidirect |
| 266. C3 | #69793 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4×C8 | 2 |
| #10592812 | 2 |
| #10592809 | 2 |
| #10592801 | 2 |
| C2×#63632 | 2 |
| #10589418 | 2 |
| #10589389 | 2 |
| #69793 | 3 |