Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1332 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1332 conjugacy classes of subgroups — too many to draw. Only its 191 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 |
|---|---|---|
| 1. #10595992 | C2 | semidirect |
| 3. #10592830 | C2 | semidirect |
| 4. C2×#63650 | C2 | semidirect |
| 5. #10592700 | C2 | semidirect |
| 6. C32×#339 | C2 | semidirect |
| 7. #10589389 | C2 | semidirect |
| 20. #64083 | C4 | semidirect |
| 30. C3×#339 | D3 | semidirect |
| 48. C2×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 54. C32×C4⋊C4 | D4 | semidirect |
| 58. C32×C42 | C2×C4 | semidirect |
| 61. C4⋊(C3⋊Dic3) | D4 | semidirect |
| 120. #339 | C3⋊D3 | semidirect |
| 143. C3×C4⋊C4 | D12 | semidirect |
| 147. C3×C42 | C4×D3 | semidirect |
| 253. C4⋊C4 | C4⋊(C3⋊D3) | semidirect |
| 260. C42 | C4×C3⋊D3 | semidirect |
| 280. C32 | #1887 | semidirect |
| 337. C3 | #68760 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10595992 | 2 |
| C2×#64083 | 2 |
| #10592830 | 2 |
| C2×#63650 | 2 |
| #10592700 | 2 |
| C32×#339 | 2 |
| #10589389 | 2 |
| #68760 | 3 |