Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
277 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 277 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 4. C3×#4517 | C2 | semidirect |
| 5. C3×#4513 | C2 | semidirect |
| 7. #69117 | C3 | direct (N × H) |
| 26. #4517 | C2×C3 | semidirect |
| 27. #4513 | C2×C3 | semidirect |
| 196. C32 | #2239 | semidirect |
| 227. C3 | #69117 | direct (N × H) |
| 228. C3 | C3×#2239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5137 | 2 |
| C3×#5125 | 2 |
| C32×#349 | 2 |
| C3×#4517 | 2 |
| C3×#4513 | 2 |
| C3×#2239 | 3 |
| #69117 | 3 |