Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
473 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 473 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×#63628 | C2 | semidirect |
| 4. C2×#63551 | C2 | semidirect |
| 6. C3×#4503 | C2 | semidirect |
| 7. #10589119 | C2 | semidirect |
| 38. #4503 | D3 | semidirect |
| 185. C2×C3×D3 | Q32 | semidirect |
| 293. C2×D3 | Dic24 | semidirect |
| 312. C32 | #2188 | semidirect |
| 356. C3 | #69113 | semidirect |
| 357. C3 | #69225 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Dic12 | 2 |
| C2×#63628 | 2 |
| #10590852 | 2 |
| C2×#63551 | 2 |
| C3×(C2×D3)⋊C16 | 2 |
| C3×#4503 | 2 |
| #10589119 | 2 |
| #69225 | 3 |
| #69113 | 3 |