Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
493 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 493 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⋊D3×#108 | C2 | semidirect |
| 3. #10590625 | C2 | semidirect |
| 4. C3×#4496 | C2 | semidirect |
| 5. C3×#4495 | C2 | semidirect |
| 6. #10589130 | C2 | semidirect |
| 7. #10589127 | C2 | semidirect |
| 40. #4496 | D3 | semidirect |
| 41. #4495 | D3 | semidirect |
| 353. C32 | #2148 | semidirect |
| 403. C3 | #69256 | semidirect |
| 404. C3 | #69266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63810 | 2 |
| C3⋊D3×#108 | 2 |
| #10590625 | 2 |
| C3×#4496 | 2 |
| C3×#4495 | 2 |
| #10589130 | 2 |
| #10589127 | 2 |
| #69266 | 3 |
| #69256 | 3 |