Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
168 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 56 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. C2×C9×D16 | C2 | semidirect |
| 2. #10588584 | C2 | semidirect |
| 3. #10588197 | C2 | semidirect |
| 4. #10588196 | C2 | semidirect |
| 5. #10588176 | C2 | semidirect |
| 12. Dic72 | C22 | semidirect |
| 14. D144 | C22 | semidirect |
| 15. C9⋊C32 | C22 | semidirect |
| 52. C2×D16 | D9 | semidirect |
| 113. C9 | #2263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×D16 | 2 |
| #10588584 | 2 |
| #10588197 | 2 |
| #10588196 | 2 |
| #10588176 | 2 |
| #71458 | 3 |