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×#500 | C2 | semidirect |
| 3. #10588760 | C2 | semidirect |
| 5. #10588558 | C2 | semidirect |
| 7. #10588362 | C2 | semidirect |
| 51. C8×D9 | Q8 | semidirect |
| 87. #500 | D9 | semidirect |
| 192. 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×#500 | 2 |
| #10588760 | 2 |
| #10588560 | 2 |
| #10588558 | 2 |
| C4×C8×D9 | 2 |
| #10588362 | 2 |
| #81938 | 3 |