Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
603 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 603 conjugacy classes of subgroups — too many to draw. Only its 134 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. #10589710 | C2 | semidirect |
| 2. C9×#466 | C2 | semidirect |
| 3. #10588838 | C2 | semidirect |
| 4. #10588791 | C2 | semidirect |
| 5. #10588788 | C2 | semidirect |
| 6. #10588718 | C2 | semidirect |
| 7. #10588564 | C2 | semidirect |
| 8. #10588463 | C2 | semidirect |
| 9. #10588454 | C2 | semidirect |
| 137. #466 | D9 | semidirect |
| 300. C9 | #3203 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589710 | 2 |
| C9×#466 | 2 |
| #10588838 | 2 |
| #10588791 | 2 |
| #10588788 | 2 |
| #10588718 | 2 |
| #10588564 | 2 |
| #10588463 | 2 |
| #10588454 | 2 |
| #80724 | 3 |