Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
297 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 297 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 |
|---|---|---|
| 2. C3×#5125 | C2 | semidirect |
| 3. C32×#349 | C2 | semidirect |
| 4. C3×#4516 | C2 | semidirect |
| 5. C3×#4513 | C2 | semidirect |
| 7. #69116 | C3 | direct (N × H) |
| 20. #5125 | C2×C3 | semidirect |
| 24. C3×#349 | D3 | semidirect |
| 25. C3×#349 | C2×C3 | semidirect |
| 26. #4516 | C2×C3 | semidirect |
| 27. #4513 | C2×C3 | semidirect |
| 79. #349 | C3×D3 | semidirect |
| 206. C32 | #2238 | semidirect |
| 242. C3 | #69116 | direct (N × H) |
| 243. C3 | C3×#2238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5135 | 2 |
| C3×#5125 | 2 |
| C32×#349 | 2 |
| C3×#4516 | 2 |
| C3×#4513 | 2 |
| C3×#2238 | 3 |
| #69116 | 3 |