Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
261 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 261 conjugacy classes of subgroups — too many to draw. Only its 68 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×SD32 | C2 | semidirect |
| 2. Q16×Dic9 | C2 | semidirect |
| 3. C2×#63387 | C2 | semidirect |
| 5. #10588239 | C2 | semidirect |
| 6. #10588186 | C2 | semidirect |
| 7. Dic9⋊C16 | C2 | semidirect |
| 35. C9×Q16 | D4 | semidirect |
| 82. C2×SD32 | D9 | semidirect |
| 120. Dic9 | SD32 | semidirect |
| 163. Q16 | #611 | semidirect |
| 190. C9 | #2207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×SD32 | 2 |
| Q16×Dic9 | 2 |
| C2×#63387 | 2 |
| #10588831 | 2 |
| #10588239 | 2 |
| #10588186 | 2 |
| Dic9⋊C16 | 2 |
| #71475 | 3 |