Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
849 conjugacy classes of subgroups; only the 298 normal subgroups are shown.
This group has 849 conjugacy classes of subgroups — too many to draw. Only its 298 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 |
|---|---|---|
| 3. C2×C3×#829 | C2 | direct (N × H) |
| 6. C22×#829 | C3 | direct (N × H) |
| 14. C3×#829 | C22 | direct (N × H) |
| 23. C2×#829 | C2×C3 | direct (N × H) |
| 60. #829 | C22×C3 | direct (N × H) |
| 113. C22×C32 | Q32 | semidirect |
| 158. C2×C32 | C2×Q32 | semidirect |
| 176. C22×C3 | #829 | direct (N × H) |
| 177. C22×C3 | C3×Q32 | semidirect |
| 191. C32 | C22×Q32 | semidirect |
| 205. C2×C3 | C2×#829 | direct (N × H) |
| 206. C2×C3 | C2×C3×Q32 | semidirect |
| 209. C22 | C3×#829 | direct (N × H) |
| 216. C3 | C22×#829 | direct (N × H) |
| 217. C3 | C22×C3×Q32 | semidirect |
| 218. C2 | C2×C3×#829 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×Q16 | 2 |
| C22×C3×Dic12 | 2 |
| C2×C3×#829 | 2 |
| C22×C3×C3⋊C16 | 2 |
| C22×C3×Q32 | 3 |
| C22×#829 | 3 |