Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
429 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 429 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
| 3. C2×#63549 | C2 | semidirect |
| 4. C3×C4⋊(C3⋊C16) | C2 | semidirect |
| 5. #10589116 | C2 | semidirect |
| 21. C4×Dic12 | D3 | semidirect |
| 28. C4⋊(C3⋊C16) | D3 | semidirect |
| 43. C3×Dic12 | D4 | semidirect |
| 119. Dic12 | D12 | semidirect |
| 136. C32×C4 | SD32 | semidirect |
| 232. C3×C4 | #800 | semidirect |
| 233. C3×C4 | #828 | semidirect |
| 240. C32 | #2207 | semidirect |
| 275. C4 | #63549 | semidirect |
| 279. C3 | #69292 | semidirect |
| 280. C3 | #70914 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592394 | 2 |
| C3×C4×Dic12 | 2 |
| C2×#63549 | 2 |
| C3×C4⋊(C3⋊C16) | 2 |
| #10589116 | 2 |
| #70914 | 3 |
| #69292 | 3 |