Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2161 conjugacy classes of subgroups; only the 428 normal subgroups are shown.
This group has 2161 conjugacy classes of subgroups — too many to draw. Only its 428 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 |
|---|---|---|
| 3. C3×C4×#217 | C2 | semidirect |
| 4. #10591705 | C2 | semidirect |
| 5. #10591233 | C2 | semidirect |
| 11. C2×#3752 | C4 | semidirect |
| 14. C2×C3×C4×Dic3 | C22 | semidirect |
| 15. #63974 | C4 | semidirect |
| 17. C2×Dic32 | C22 | semidirect |
| 18. C3×C3⋊#95 | C22 | semidirect |
| 19. #63579 | C22 | semidirect |
| 24. C4×#217 | D3 | semidirect |
| 35. C22×C32×C4 | C2×C4 | semidirect |
| 38. C22×C3⋊Dic3 | C2×C4 | semidirect |
| 43. C2×#624 | C2×C4 | semidirect |
| 44. #3752 | C2×C4 | semidirect |
| 45. C3×#217 | C2×C4 | semidirect |
| 47. #3722 | C2×C4 | semidirect |
| 67. C2×C4×Dic3 | C2×D3 | semidirect |
| 71. C3⋊#95 | C2×D3 | semidirect |
| 82. C22×C3⋊D3 | C42 | semidirect |
| 118. C22×C3×C4 | C4×D3 | semidirect |
| 133. #217 | C4×D3 | semidirect |
| 239. C22×C4 | #624 | semidirect |
| 281. C32 | #2273 | semidirect |
| 336. C3 | #73560 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3752 | 2 |
| C2×#63974 | 2 |
| C3×C4×#217 | 2 |
| #10591705 | 2 |
| #10591233 | 2 |
| #73560 | 3 |