Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1944 conjugacy classes of subgroups; only the 337 normal subgroups are shown.
This group has 1944 conjugacy classes of subgroups — too many to draw. Only its 337 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. C32×#383 | C2 | semidirect |
| 3. #10592636 | C2 | semidirect |
| 4. #10592364 | C2 | semidirect |
| 10. #64083 | C4 | semidirect |
| 14. C3×#383 | D3 | semidirect |
| 23. C2×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 25. C32×C42 | C2×C4 | semidirect |
| 48. #383 | C3⋊D3 | semidirect |
| 57. C3×C42 | C4×D3 | semidirect |
| 96. C42 | C4×C3⋊D3 | semidirect |
| 105. C32 | #2380 | semidirect |
| 127. C3 | #74298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64083 | 2 |
| C32×#383 | 2 |
| #10592636 | 2 |
| #10592364 | 2 |
| #74298 | 3 |