Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
567 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 567 conjugacy classes of subgroups — too many to draw. Only its 134 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×#467 | C2 | semidirect |
| 3. #10588866 | C2 | semidirect |
| 5. #10588788 | C2 | semidirect |
| 6. #10588728 | C2 | semidirect |
| 7. #10588568 | C2 | semidirect |
| 8. #10588494 | C2 | semidirect |
| 9. #10588489 | C2 | semidirect |
| 134. #467 | D9 | semidirect |
| 289. C9 | #3202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589730 | 2 |
| C9×#467 | 2 |
| #10588866 | 2 |
| #10588791 | 2 |
| #10588788 | 2 |
| #10588728 | 2 |
| #10588568 | 2 |
| #10588494 | 2 |
| #10588489 | 2 |
| #80767 | 3 |