Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
329 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 329 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 17. C3×#829 | C4 | semidirect |
| 71. #829 | Dic3 | direct (N × H) |
| 151. C3×Dic3 | Q32 | semidirect |
| 241. Dic3 | #829 | direct (N × H) |
| 242. C32 | C4×Q32 | semidirect |
| 276. C3 | C4×#829 | semidirect |
| 277. C3 | Dic3×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Dic3×Q16 | 2 |
| C2×C3×#829 | 2 |
| Dic3×Dic12 | 2 |
| #10589430 | 2 |
| #10589139 | 2 |
| #10589117 | 2 |
| Dic3×C3⋊C16 | 2 |
| Dic3×Q32 | 3 |
| C4×#829 | 3 |