Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
603 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 603 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 |
|---|---|---|
| 1. #10589731 | C2 | semidirect |
| 2. C9×#467 | C2 | semidirect |
| 3. #10588867 | C2 | semidirect |
| 4. #10588796 | C2 | semidirect |
| 5. #10588791 | C2 | semidirect |
| 6. #10588732 | C2 | semidirect |
| 7. #10588562 | C2 | semidirect |
| 8. #10588491 | C2 | semidirect |
| 9. #10588490 | C2 | semidirect |
| 136. #467 | D9 | semidirect |
| 300. C9 | #3203 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589731 | 2 |
| C9×#467 | 2 |
| #10588867 | 2 |
| #10588796 | 2 |
| #10588791 | 2 |
| #10588732 | 2 |
| #10588562 | 2 |
| #10588491 | 2 |
| #10588490 | 2 |
| #80768 | 3 |