Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
347 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 347 conjugacy classes of subgroups — too many to draw. Only its 92 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×C8×Dic6 | C2 | semidirect |
| 4. #10590310 | C2 | semidirect |
| 5. #10589323 | C2 | semidirect |
| 6. #10589095 | C2 | semidirect |
| 32. C8×Dic6 | D3 | semidirect |
| 282. C32 | #1678 | semidirect |
| 327. C3 | #70940 | semidirect |
| 328. C3 | #71208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4694 | 2 |
| C3×C8×Dic6 | 2 |
| #10590364 | 2 |
| #10590310 | 2 |
| #10589323 | 2 |
| #10589095 | 2 |
| #10589090 | 2 |
| #71208 | 3 |
| #70940 | 3 |