Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
485 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 485 conjugacy classes of subgroups — too many to draw. Only its 116 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×#4682 | C2 | semidirect |
| 3. #10590375 | C2 | semidirect |
| 4. #10590277 | C2 | semidirect |
| 5. C8×C3⋊(C3⋊C8) | C2 | semidirect |
| 24. #4682 | D3 | semidirect |
| 71. C32×C8 | SD16 | semidirect |
| 73. C3⋊(C3⋊C8) | D8 | semidirect |
| 146. C3×C8 | #214 | semidirect |
| 147. C3×C8 | #215 | semidirect |
| 190. C32 | #1706 | semidirect |
| 202. C8 | #3715 | semidirect |
| 223. C3 | #71274 | semidirect |
| 224. C3 | #71359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4695 | 2 |
| C3×#4682 | 2 |
| #10590375 | 2 |
| #10590277 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| #71359 | 3 |
| #71274 | 3 |