Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
648 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 181 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. C32×C4×M16 | C2 | semidirect |
| 4. #10592823 | C2 | semidirect |
| 6. #10589425 | C2 | semidirect |
| 7. #10589389 | C2 | semidirect |
| 19. #63651 | C4 | semidirect |
| 20. #63650 | C4 | semidirect |
| 24. C3×C4×M16 | D3 | semidirect |
| 104. C4×M16 | C3⋊D3 | semidirect |
| 236. C32 | #1932 | semidirect |
| 281. C3 | #69874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×M16 | 2 |
| #10592838 | 2 |
| #10592831 | 2 |
| #10592823 | 2 |
| C2×#63632 | 2 |
| #10589425 | 2 |
| #10589389 | 2 |
| #69874 | 3 |