Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2049 conjugacy classes of subgroups; only the 276 normal subgroups are shown.
This group has 2049 conjugacy classes of subgroups — too many to draw. Only its 276 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. #10594996 | C2 | semidirect |
| 3. C3×#5240 | C2 | semidirect |
| 4. #10591527 | C2 | semidirect |
| 5. #10591232 | C2 | semidirect |
| 9. C2×#3832 | C4 | semidirect |
| 10. C2×D4×C3⋊D3 | C4 | semidirect |
| 12. C2×#3828 | C4 | semidirect |
| 14. C22×C4⋊(C3⋊D3) | C4 | semidirect |
| 16. C3×#926 | C22 | semidirect |
| 17. #63974 | C22 | semidirect |
| 19. C3×#834 | C22 | semidirect |
| 20. #63581 | C22 | semidirect |
| 25. #5240 | D3 | semidirect |
| 28. C23×C3⋊D3 | C2×C4 | semidirect |
| 31. C2×C32×Q8 | C2×C4 | semidirect |
| 32. C2×C32×D4 | C2×C4 | semidirect |
| 34. C22×C32×C4 | C2×C4 | semidirect |
| 36. C2×#638 | C2×C4 | semidirect |
| 46. C2×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 47. C2×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 49. C2×C4×C3⋊D3 | C2×C4 | semidirect |
| 50. C2×C4×C3⋊D3 | C2×C4 | semidirect |
| 51. C2×#634 | C2×C4 | semidirect |
| 78. #926 | C2×D3 | semidirect |
| 83. #834 | C2×D3 | semidirect |
| 126. C2×C3×Q8 | C4×D3 | semidirect |
| 129. C2×C3×D4 | C4×D3 | semidirect |
| 133. C22×C3×C4 | C4×D3 | semidirect |
| 282. C2×Q8 | #624 | semidirect |
| 293. C2×D4 | #624 | semidirect |
| 298. C22×C4 | #624 | semidirect |
| 337. C32 | #2883 | semidirect |
| 395. C3 | #78694 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64366 | 2 |
| #10594996 | 2 |
| C3×#5240 | 2 |
| #10591527 | 2 |
| #10591232 | 2 |
| #78694 | 3 |