Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
534 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 170 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×#499 | C2 | semidirect |
| 3. #10588744 | C2 | semidirect |
| 5. #10588554 | C2 | semidirect |
| 7. #10588535 | C2 | semidirect |
| 9. #10588363 | C2 | semidirect |
| 56. C8×D9 | Q8 | semidirect |
| 57. C8×D9 | Q8 | semidirect |
| 97. #499 | D9 | semidirect |
| 197. C9 | #3160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589790 | 2 |
| C9×#499 | 2 |
| #10588744 | 2 |
| #10588560 | 2 |
| #10588554 | 2 |
| #10588540 | 2 |
| #10588535 | 2 |
| C4×C8×D9 | 2 |
| #10588363 | 2 |
| #81916 | 3 |