Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
429 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 429 conjugacy classes of subgroups — too many to draw. Only its 78 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. C2×C3×#827 | C2 | semidirect |
| 3. #10590818 | C2 | semidirect |
| 4. C2×#63549 | C2 | semidirect |
| 5. C3×#4562 | C2 | semidirect |
| 6. #10589133 | C2 | semidirect |
| 7. #10589116 | C2 | semidirect |
| 29. C2×#827 | D3 | semidirect |
| 33. #4562 | D3 | semidirect |
| 53. C3×Dic12 | D4 | semidirect |
| 156. Dic12 | #67 | semidirect |
| 177. C3⋊Dic3 | SD32 | semidirect |
| 305. C32 | #2207 | semidirect |
| 353. C3 | #69204 | semidirect |
| 354. C3 | #71475 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592850 | 2 |
| C2×C3×#827 | 2 |
| #10590818 | 2 |
| C2×#63549 | 2 |
| C3×#4562 | 2 |
| #10589133 | 2 |
| #10589116 | 2 |
| #71475 | 3 |
| #69204 | 3 |