Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
508 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 1. C23×C3×C16 | C2 | semidirect |
| 3. #71963 | C2 | semidirect |
| 4. C2×#4508 | C2 | semidirect |
| 5. #67805 | C2 | semidirect |
| 22. C23×C16 | D3 | semidirect |
| 50. C2×C3×C16 | D4 | semidirect |
| 138. C2×C16 | #67 | semidirect |
| 214. C22×C3 | #350 | semidirect |
| 264. C22 | #4508 | semidirect |
| 273. C3 | #12983 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C16 | 2 |
| #83734 | 2 |
| #71963 | 2 |
| C2×#4508 | 2 |
| #67805 | 2 |
| #12983 | 3 |