Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
541 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 541 conjugacy classes of subgroups — too many to draw. Only its 90 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×#4851 | C2 | semidirect |
| 3. #10590379 | C2 | semidirect |
| 4. #10590277 | C2 | semidirect |
| 5. #10589349 | C2 | semidirect |
| 6. C3×#4485 | C2 | semidirect |
| 7. #10589083 | C2 | semidirect |
| 33. #4851 | D3 | semidirect |
| 37. #4485 | D3 | semidirect |
| 126. C3×Dic6 | SD16 | semidirect |
| 288. Dic6 | #215 | semidirect |
| 369. C32 | #1642 | semidirect |
| 429. C3 | #68393 | semidirect |
| 430. C3 | #71124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593900 | 2 |
| C3×#4851 | 2 |
| #10590379 | 2 |
| #10590277 | 2 |
| #10589349 | 2 |
| C3×#4485 | 2 |
| #10589083 | 2 |
| #71124 | 3 |
| #68393 | 3 |