Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
243 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 243 conjugacy classes of subgroups — too many to draw. Only its 92 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. Q16×Dic9 | C2 | semidirect |
| 4. #10588241 | C2 | semidirect |
| 6. #10588182 | C2 | semidirect |
| 7. C16×Dic9 | C2 | semidirect |
| 13. C9×SD32 | C4 | semidirect |
| 32. C9×Q16 | C2×C4 | semidirect |
| 43. C9×C16 | C2×C4 | semidirect |
| 107. Dic9 | SD32 | direct (N × H) |
| 112. SD32 | Dic9 | direct (N × H) |
| 143. Q16 | C2×Dic9 | semidirect |
| 155. C16 | C2×Dic9 | semidirect |
| 167. C9 | C4×SD32 | 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 |
| D8×Dic9 | 2 |
| #10588241 | 2 |
| #10588239 | 2 |
| #10588182 | 2 |
| C16×Dic9 | 2 |
| Dic3×SD32 | 3 |