Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
363 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 363 conjugacy classes of subgroups — too many to draw. Only its 96 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×#4679 | C2 | semidirect |
| 4. #10590285 | C2 | semidirect |
| 5. #10589324 | C2 | semidirect |
| 6. #10589093 | C2 | semidirect |
| 32. #4679 | D3 | semidirect |
| 110. C32×C8 | SD16 | semidirect |
| 231. C3×C8 | #214 | semidirect |
| 232. C3×C8 | #215 | semidirect |
| 293. C32 | #1686 | semidirect |
| 314. C8 | #3715 | semidirect |
| 339. C3 | #70958 | semidirect |
| 340. C3 | #71273 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4693 | 2 |
| C3×#4679 | 2 |
| #10590364 | 2 |
| #10590285 | 2 |
| #10589324 | 2 |
| #10589093 | 2 |
| #10589090 | 2 |
| #71273 | 3 |
| #70958 | 3 |