Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
525 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 525 conjugacy classes of subgroups — too many to draw. Only its 136 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. #10589868 | C2 | semidirect |
| 2. C2×C9×Q32 | C2 | semidirect |
| 3. #10588859 | C2 | semidirect |
| 4. #10588599 | C2 | semidirect |
| 5. #10588598 | C2 | semidirect |
| 6. D9×Q32 | C2 | semidirect |
| 7. #10588584 | C2 | semidirect |
| 8. #10588581 | C2 | semidirect |
| 104. C2×Q32 | D9 | semidirect |
| 208. C9 | #3417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589868 | 2 |
| C2×C9×Q32 | 2 |
| #10588859 | 2 |
| #10588599 | 2 |
| #10588598 | 2 |
| D9×Q32 | 2 |
| #10588584 | 2 |
| #10588581 | 2 |
| #82028 | 3 |