Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
3525 conjugacy classes of subgroups; only the 996 normal subgroups are shown.
This group has 3525 conjugacy classes of subgroups — too many to draw. Only its 996 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. C3×#5812 | C2 | semidirect |
| 3. #10595386 | C2 | semidirect |
| 4. #10595353 | C2 | semidirect |
| 5. #10594996 | C2 | semidirect |
| 6. #10594969 | C2 | semidirect |
| 9. C2×#3832 | C4 | semidirect |
| 14. C3×Q8×Dic3 | C22 | semidirect |
| 18. #63900 | C22 | semidirect |
| 19. #63894 | C22 | semidirect |
| 20. C4×#624 | C22 | semidirect |
| 21. #63874 | C22 | semidirect |
| 22. #63849 | C22 | semidirect |
| 26. #5812 | D3 | semidirect |
| 32. C2×C32×Q8 | C2×C4 | semidirect |
| 36. #3832 | C2×C4 | semidirect |
| 37. #3832 | C2×C4 | semidirect |
| 38. C2×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 40. C2×C4×C3⋊D3 | C2×C4 | semidirect |
| 65. Q8×Dic3 | C2×D3 | semidirect |
| 100. C2×C3×Q8 | C4×D3 | semidirect |
| 191. C2×Q8 | #624 | semidirect |
| 227. C32 | #3428 | semidirect |
| 262. C3 | #85872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3832 | 2 |
| C3×#5812 | 2 |
| #10595386 | 2 |
| #10595353 | 2 |
| #10594996 | 2 |
| #10594969 | 2 |
| #85872 | 3 |