Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
548 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 548 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. #81934 | C2 | semidirect |
| 3. C3×#2252 | C2 | semidirect |
| 4. #71382 | C2 | semidirect |
| 5. #71381 | C2 | semidirect |
| 6. #69329 | C2 | semidirect |
| 7. #69319 | C2 | semidirect |
| 8. #69061 | C2 | semidirect |
| 9. C4×#798 | C2 | semidirect |
| 38. #2252 | D3 | semidirect |
| 147. C3×C16 | #41 | semidirect |
| 256. C16 | #239 | semidirect |
| 325. C3 | #33751 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #81934 | 2 |
| #81933 | 2 |
| C3×#2252 | 2 |
| #71382 | 2 |
| #71381 | 2 |
| #69329 | 2 |
| #69319 | 2 |
| #69061 | 2 |
| C4×#798 | 2 |
| #33751 | 3 |