Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1091 conjugacy classes of subgroups; only the 326 normal subgroups are shown.
This group has 1091 conjugacy classes of subgroups — too many to draw. Only its 326 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. C32×#401 | C2 | semidirect |
| 3. C3×C3⋊#401 | C2 | semidirect |
| 5. D3×#401 | C3 | direct (N × H) |
| 11. C3×#401 | D3 | direct (N × H) |
| 12. C3×#401 | C2×C3 | semidirect |
| 15. C3⋊#401 | C2×C3 | semidirect |
| 34. #401 | C3×D3 | direct (N × H) |
| 65. C3×D3 | #401 | direct (N × H) |
| 80. C32 | C2×#401 | semidirect |
| 90. D3 | C3×#401 | direct (N × H) |
| 96. C3 | D3×#401 | direct (N × H) |
| 97. C3 | C2×C3×#401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#401 | 2 |
| C3×D3×#95 | 2 |
| C3×C3⋊#401 | 2 |
| C2×C3×#401 | 3 |
| D3×#401 | 3 |