Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
540 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 146 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. #10589834 | C2 | semidirect |
| 2. C9×#494 | C2 | semidirect |
| 4. #10588865 | C2 | semidirect |
| 5. Q16×Dic9 | C2 | semidirect |
| 6. #10588768 | C2 | semidirect |
| 8. C8×Dic18 | C2 | semidirect |
| 99. #494 | D9 | semidirect |
| 215. C9 | #3393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589834 | 2 |
| C9×#494 | 2 |
| #10588871 | 2 |
| #10588865 | 2 |
| Q16×Dic9 | 2 |
| #10588768 | 2 |
| C4×D72 | 2 |
| C8×Dic18 | 2 |
| #81795 | 3 |