Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
395 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 395 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 |
| 3. #10590364 | C2 | semidirect |
| 4. #10589323 | C2 | semidirect |
| 5. #10589090 | C2 | semidirect |
| 24. #4679 | D3 | semidirect |
| 83. C32×C8 | SD16 | semidirect |
| 178. C3×C8 | #214 | semidirect |
| 179. C3×C8 | #215 | semidirect |
| 228. C32 | #1688 | semidirect |
| 244. C8 | #3715 | semidirect |
| 267. C3 | #70959 | semidirect |
| 268. C3 | #71287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4695 | 2 |
| C3×#4679 | 2 |
| #10590364 | 2 |
| #10589323 | 2 |
| #10589090 | 2 |
| #71287 | 3 |
| #70959 | 3 |