Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1033 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 1033 conjugacy classes of subgroups — too many to draw. Only its 234 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 |
|---|---|---|
| 4. C3×#4716 | C2 | semidirect |
| 5. #10590819 | C2 | semidirect |
| 6. #10590791 | C2 | semidirect |
| 9. #10590381 | C2 | semidirect |
| 24. #63802 | C4 | semidirect |
| 42. #4716 | D3 | semidirect |
| 65. C3×Dic12 | C2×C4 | semidirect |
| 69. #3718 | C2×C4 | semidirect |
| 172. Dic12 | C4×D3 | semidirect |
| 246. C3⋊D3 | #441 | semidirect |
| 292. C32 | C2×#441 | semidirect |
| 329. C3 | D3×#441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63802 | 2 |
| C4×#3797 | 2 |
| C3⋊D3×#97 | 2 |
| C3×#4716 | 2 |
| #10590819 | 2 |
| #10590791 | 2 |
| #10590685 | 2 |
| #10590672 | 2 |
| #10590381 | 2 |
| D3×#441 | 3 |