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. #10589873 | C2 | semidirect |
| 2. C9×#508 | C2 | semidirect |
| 3. #10588875 | C2 | semidirect |
| 4. D9×Q32 | C2 | semidirect |
| 5. #10588595 | C2 | semidirect |
| 6. #10588592 | C2 | semidirect |
| 7. C2×Dic72 | C2 | semidirect |
| 8. #10588581 | C2 | semidirect |
| 102. #508 | 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 |
|---|---|
| #10589873 | 2 |
| C9×#508 | 2 |
| #10588875 | 2 |
| D9×Q32 | 2 |
| #10588595 | 2 |
| #10588592 | 2 |
| C2×Dic72 | 2 |
| #10588581 | 2 |
| #82033 | 3 |