Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
534 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 178 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 |
|---|---|---|
| 2. C9×#498 | C2 | semidirect |
| 3. #10588758 | C2 | semidirect |
| 5. #10588538 | C2 | semidirect |
| 7. #10588360 | C2 | semidirect |
| 49. C8×D9 | Q8 | semidirect |
| 84. #498 | D9 | semidirect |
| 173. C9 | #3160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589830 | 2 |
| C9×#498 | 2 |
| #10588758 | 2 |
| #10588540 | 2 |
| #10588538 | 2 |
| C4×C8×D9 | 2 |
| #10588360 | 2 |
| #81891 | 3 |