Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
575 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 575 conjugacy classes of subgroups — too many to draw. Only its 126 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×#825 | C2 | semidirect |
| 3. C3×#5132 | C2 | semidirect |
| 4. C3×#5118 | C2 | semidirect |
| 5. C32×#338 | C2 | semidirect |
| 7. #68719 | C3 | direct (N × H) |
| 26. C2×#825 | C2×C3 | semidirect |
| 27. #5132 | C2×C3 | semidirect |
| 28. #5118 | C2×C3 | semidirect |
| 30. C3×#338 | D3 | semidirect |
| 31. C3×#338 | C2×C3 | semidirect |
| 109. #338 | C3×D3 | semidirect |
| 290. C32 | #2050 | semidirect |
| 335. C3 | #68719 | direct (N × H) |
| 336. C3 | C3×#2050 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5748 | 2 |
| C2×C3×#825 | 2 |
| C3×#5132 | 2 |
| C3×#5118 | 2 |
| C32×#338 | 2 |
| C3×#2050 | 3 |
| #68719 | 3 |