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×#470 | C2 | semidirect |
| 3. #10588866 | C2 | semidirect |
| 5. #10588807 | C2 | semidirect |
| 6. #10588727 | C2 | semidirect |
| 7. #10588548 | C2 | semidirect |
| 8. #10588495 | C2 | semidirect |
| 9. #10588489 | C2 | semidirect |
| 133. #470 | D9 | semidirect |
| 284. 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×#470 | 2 |
| #10588866 | 2 |
| #10588811 | 2 |
| #10588807 | 2 |
| #10588727 | 2 |
| #10588548 | 2 |
| #10588495 | 2 |
| #10588489 | 2 |
| #80912 | 3 |