Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
336 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 101 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. C32×#508 | C2 | semidirect |
| 2. C2×#63626 | C2 | semidirect |
| 3. #10589387 | C2 | semidirect |
| 4. #10589385 | C2 | semidirect |
| 5. #10589365 | C2 | semidirect |
| 9. C32×Q32 | C22 | semidirect |
| 11. C32×D16 | C22 | semidirect |
| 15. C3⋊(C3⋊C32) | C22 | semidirect |
| 16. C3×#508 | D3 | semidirect |
| 34. C3×Q32 | C2×D3 | semidirect |
| 36. C3×D16 | C2×D3 | semidirect |
| 51. #508 | C3⋊D3 | semidirect |
| 75. Q32 | C2×C3⋊D3 | semidirect |
| 79. D16 | C2×C3⋊D3 | semidirect |
| 113. C32 | #2263 | semidirect |
| 135. C3 | #71509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#508 | 2 |
| C2×#63626 | 2 |
| #10589387 | 2 |
| #10589385 | 2 |
| #10589365 | 2 |
| #71509 | 3 |