Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
452 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 89 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. #79342 | C2 | semidirect |
| 3. C3×#1496 | C2 | semidirect |
| 4. #71816 | C2 | semidirect |
| 5. #70788 | C2 | semidirect |
| 6. #67748 | C2 | semidirect |
| 7. #67743 | C2 | semidirect |
| 15. #5089 | C4 | semidirect |
| 16. #5081 | C4 | semidirect |
| 17. #5074 | C4 | semidirect |
| 18. #5071 | C4 | semidirect |
| 40. #1496 | D3 | semidirect |
| 424. C3 | #8997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83292 | 2 |
| #79342 | 2 |
| C3×#1496 | 2 |
| #71816 | 2 |
| #70788 | 2 |
| #67748 | 2 |
| #67743 | 2 |
| #8997 | 3 |