Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
391 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 391 conjugacy classes of subgroups — too many to draw. Only its 106 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. C3×C4×Dic12 | C2 | semidirect |
| 4. C3×C4×C3⋊C16 | C2 | semidirect |
| 5. #10589141 | C2 | semidirect |
| 6. #10589118 | C2 | semidirect |
| 21. #63549 | C4 | direct (N × H) |
| 25. C4×Dic12 | D3 | semidirect |
| 36. C4×C3⋊C16 | D3 | semidirect |
| 51. C3×Dic12 | C2×C4 | semidirect |
| 53. C3×C3⋊C16 | C2×C4 | semidirect |
| 138. Dic12 | C4×D3 | semidirect |
| 148. C3⋊C16 | C4×D3 | semidirect |
| 154. C32×C4 | SD32 | semidirect |
| 254. C3×C4 | #800 | semidirect |
| 255. C3×C4 | #828 | semidirect |
| 265. C32 | C4×SD32 | semidirect |
| 301. C4 | #63549 | direct (N × H) |
| 305. C3 | C4×#800 | semidirect |
| 306. C3 | C4×#828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3745 | 2 |
| C3×C4×Dic12 | 2 |
| C2×#63549 | 2 |
| C3×C4×C3⋊C16 | 2 |
| #10589141 | 2 |
| #10589118 | 2 |
| #10589116 | 2 |
| C4×#828 | 3 |
| C4×#800 | 3 |