Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
311 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 311 conjugacy classes of subgroups — too many to draw. Only its 102 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×#5184 | C2 | semidirect |
| 4. C32×#362 | C2 | semidirect |
| 6. C3×#4512 | C2 | semidirect |
| 7. C3×#4494 | C2 | semidirect |
| 9. #69264 | C3 | direct (N × H) |
| 17. C3×#829 | C4 | semidirect |
| 18. C3×#828 | C4 | semidirect |
| 26. #5184 | C2×C3 | semidirect |
| 31. C3×#362 | D3 | semidirect |
| 32. C3×#362 | C2×C3 | semidirect |
| 36. #4512 | C2×C3 | semidirect |
| 37. #4494 | C2×C3 | semidirect |
| 80. #829 | C3×C4 | semidirect |
| 81. #828 | C3×C4 | semidirect |
| 104. #362 | C3×D3 | semidirect |
| 246. C32 | #2180 | semidirect |
| 278. C3 | #69264 | direct (N × H) |
| 279. C3 | C3×#2180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5184 | 2 |
| C3×#5179 | 2 |
| C3×#4894 | 2 |
| C32×#362 | 2 |
| C3×#4518 | 2 |
| C3×#4512 | 2 |
| C3×#4494 | 2 |
| C3×#2180 | 3 |
| #69264 | 3 |