Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
359 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 359 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 |
| 3. #10590384 | C2 | semidirect |
| 5. #10589324 | C2 | semidirect |
| 6. #10589092 | C2 | semidirect |
| 32. C8×Dic6 | D3 | semidirect |
| 289. C32 | #1682 | semidirect |
| 335. C3 | #70941 | semidirect |
| 336. C3 | #71209 | 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 |
| #10590384 | 2 |
| #10590364 | 2 |
| #10589324 | 2 |
| #10589092 | 2 |
| #10589090 | 2 |
| #71209 | 3 |
| #70941 | 3 |