Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
390 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 118 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. C2×C9×M32 | C2 | semidirect |
| 3. #10588787 | C2 | semidirect |
| 4. #10588186 | C2 | semidirect |
| 11. C2×D72 | C4 | semidirect |
| 14. C2×C9×C16 | C22 | semidirect |
| 15. #63378 | C22 | semidirect |
| 66. C2×M32 | D9 | semidirect |
| 104. C2×C16 | C2×D9 | semidirect |
| 153. C9 | #2140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D72 | 2 |
| C2×C9×M32 | 2 |
| #10588787 | 2 |
| #10588186 | 2 |
| #71440 | 3 |