Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
802 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 802 conjugacy classes of subgroups — too many to draw. Only its 235 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. C2×#4681 | C2 | semidirect |
| 3. C2×C3×C82 | C2 | semidirect |
| 4. #68061 | C2 | direct (N × H) |
| 14. #4681 | C22 | semidirect |
| 15. C3×C82 | C22 | semidirect |
| 19. C2×C82 | D3 | semidirect |
| 45. C82 | C2×D3 | semidirect |
| 129. C2×C3 | #1711 | semidirect |
| 139. C3 | C2×#1711 | semidirect |
| 141. C2 | #68061 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4681 | 2 |
| C2×#4694 | 2 |
| C2×C3×C82 | 2 |
| #68061 | 2 |
| C2×#1711 | 3 |