Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
249 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 249 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 4. #10588360 | C2 | semidirect |
| 5. C9×#334 | C2 | semidirect |
| 6. #10588159 | C2 | semidirect |
| 7. #10588158 | C2 | semidirect |
| 82. C8×C9 | SD16 | semidirect |
| 88. #334 | D9 | semidirect |
| 189. C9 | #1671 | semidirect |
| 208. C8 | #3664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10588526 | 2 |
| #10588525 | 2 |
| C8×D36 | 2 |
| #10588360 | 2 |
| C9×#334 | 2 |
| #10588159 | 2 |
| #10588158 | 2 |
| #68537 | 3 |