Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
690 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 154 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. #10589655 | C2 | semidirect |
| 2. C4×C9×D8 | C2 | semidirect |
| 3. #10588831 | C2 | semidirect |
| 4. #10588698 | C2 | semidirect |
| 5. #10588552 | C2 | semidirect |
| 6. #10588466 | C2 | semidirect |
| 7. #10588377 | C2 | semidirect |
| 8. C8×Dic18 | C2 | semidirect |
| 99. Dic18 | D8 | semidirect |
| 101. C8×C9 | #41 | semidirect |
| 110. C4×D8 | D9 | semidirect |
| 233. C9 | #3391 | semidirect |
| 255. C8 | #3697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589655 | 2 |
| C4×C9×D8 | 2 |
| #10588831 | 2 |
| #10588698 | 2 |
| #10588552 | 2 |
| #10588466 | 2 |
| #10588377 | 2 |
| C8×Dic18 | 2 |
| #79578 | 3 |