Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
481 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 481 conjugacy classes of subgroups — too many to draw. Only its 98 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. C3×#5748 | C2 | semidirect |
| 2. C3×#5135 | C2 | semidirect |
| 3. C3×#4908 | C2 | semidirect |
| 4. C32×#349 | C2 | semidirect |
| 5. C3×#4518 | C2 | semidirect |
| 7. #69120 | C3 | direct (N × H) |
| 15. C2×C3×D24 | C22 | semidirect |
| 16. C32×M32 | C22 | semidirect |
| 18. C3×#817 | C22 | semidirect |
| 22. #5748 | C2×C3 | semidirect |
| 25. #5135 | C2×C3 | semidirect |
| 26. #4908 | C2×C3 | semidirect |
| 29. C3×#349 | D3 | semidirect |
| 30. C3×#349 | C2×C3 | semidirect |
| 31. #4518 | C2×C3 | semidirect |
| 49. C3×Dic12 | D4 | semidirect |
| 52. C3×D24 | D4 | semidirect |
| 73. C2×D24 | C22×C3 | semidirect |
| 77. C3×M32 | C2×D3 | semidirect |
| 78. C3×M32 | C22×C3 | semidirect |
| 82. #817 | C22×C3 | semidirect |
| 111. #349 | C3×D3 | semidirect |
| 156. Dic12 | C3×D4 | semidirect |
| 159. D24 | C3×D4 | semidirect |
| 188. M32 | C2×C3×D3 | semidirect |
| 303. C32 | #2190 | semidirect |
| 353. C3 | #69120 | direct (N × H) |
| 354. C3 | C3×#2190 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5748 | 2 |
| C3×#5135 | 2 |
| C3×#4908 | 2 |
| C32×#349 | 2 |
| C3×#4518 | 2 |
| C3×#2190 | 3 |
| #69120 | 3 |