Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
485 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 485 conjugacy classes of subgroups — too many to draw. Only its 154 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×#4694 | C2 | semidirect |
| 3. C3×#4693 | C2 | semidirect |
| 4. C3×#4682 | C2 | semidirect |
| 5. C32×C82 | C2 | semidirect |
| 7. #68058 | C3 | direct (N × H) |
| 22. #4694 | C2×C3 | semidirect |
| 23. #4693 | C2×C3 | semidirect |
| 24. #4682 | C2×C3 | semidirect |
| 26. C3×C82 | D3 | semidirect |
| 27. C3×C82 | C2×C3 | semidirect |
| 72. C32×C8 | D8 | semidirect |
| 73. C32×C8 | SD16 | semidirect |
| 78. C82 | C3×D3 | semidirect |
| 150. C3×C8 | #204 | semidirect |
| 151. C3×C8 | D24 | semidirect |
| 152. C3×C8 | C3×D8 | semidirect |
| 153. C3×C8 | C3×SD16 | semidirect |
| 190. C32 | #1706 | semidirect |
| 201. C8 | C3×#204 | semidirect |
| 202. C8 | C3×D24 | semidirect |
| 223. C3 | #68058 | direct (N × H) |
| 224. C3 | C3×#1706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4695 | 2 |
| C3×#4694 | 2 |
| C3×#4693 | 2 |
| C3×#4682 | 2 |
| C32×C82 | 2 |
| C3×#1706 | 3 |
| #68058 | 3 |