Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
656 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 656 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×#5020 | C2 | semidirect |
| 3. #10590379 | C2 | semidirect |
| 4. #10590281 | C2 | semidirect |
| 5. C3×#4535 | C2 | semidirect |
| 6. #10589091 | C2 | semidirect |
| 7. #10589082 | C2 | semidirect |
| 33. #5020 | D3 | semidirect |
| 37. #4535 | D3 | semidirect |
| 113. C32×Q8 | SD16 | semidirect |
| 258. C3×Q8 | #204 | semidirect |
| 259. C3×Q8 | #215 | semidirect |
| 401. C32 | #1642 | semidirect |
| 407. Q8 | #3717 | semidirect |
| 462. C3 | #68248 | semidirect |
| 463. C3 | #71124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596048 | 2 |
| C3×#5020 | 2 |
| #10590379 | 2 |
| #10590281 | 2 |
| C3×#4535 | 2 |
| #10589091 | 2 |
| #10589082 | 2 |
| #71124 | 3 |
| #68248 | 3 |