Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
333 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 333 conjugacy classes of subgroups — too many to draw. Only its 106 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. C2×C3×#818 | C2 | semidirect |
| 3. C32×C22⋊C16 | C2 | semidirect |
| 4. C3×#4509 | C2 | semidirect |
| 5. C3×#4504 | C2 | semidirect |
| 7. #69095 | C3 | direct (N × H) |
| 20. C2×#818 | C2×C3 | semidirect |
| 24. C3×C22⋊C16 | D3 | semidirect |
| 25. C3×C22⋊C16 | C2×C3 | semidirect |
| 26. #4509 | C2×C3 | semidirect |
| 27. #4504 | C2×C3 | semidirect |
| 80. C22⋊C16 | C3×D3 | semidirect |
| 217. C32 | #2232 | semidirect |
| 259. C3 | #69095 | direct (N × H) |
| 260. C3 | C3×#2232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5115 | 2 |
| C2×C3×#818 | 2 |
| C32×C22⋊C16 | 2 |
| C3×#4509 | 2 |
| C3×#4504 | 2 |
| C3×#2232 | 3 |
| #69095 | 3 |