Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
357 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 357 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 |
|---|---|---|
| 3. Dic3×Dic12 | C2 | semidirect |
| 5. #10589141 | C2 | semidirect |
| 6. #10589117 | C2 | semidirect |
| 7. Dic3×C3⋊C16 | C2 | semidirect |
| 17. C3×#827 | C4 | semidirect |
| 49. C3×Dic12 | C2×C4 | semidirect |
| 53. C3×C3⋊C16 | C2×C4 | semidirect |
| 71. #827 | Dic3 | direct (N × H) |
| 138. Dic12 | C2×Dic3 | semidirect |
| 143. C3⋊C16 | C2×Dic3 | semidirect |
| 154. C3×Dic3 | SD32 | semidirect |
| 253. Dic3 | #827 | direct (N × H) |
| 254. C32 | C4×SD32 | semidirect |
| 294. C3 | C4×#827 | semidirect |
| 295. C3 | Dic3×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Dic3×D8 | 2 |
| C2×C3×#827 | 2 |
| Dic3×Dic12 | 2 |
| #10589428 | 2 |
| #10589141 | 2 |
| #10589117 | 2 |
| Dic3×C3⋊C16 | 2 |
| Dic3×SD32 | 3 |
| C4×#827 | 3 |