Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
452 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. C3×#1506 | C2 | semidirect |
| 4. #71821 | C2 | semidirect |
| 6. #67754 | C2 | semidirect |
| 7. #67615 | C2 | semidirect |
| 13. #5091 | C4 | semidirect |
| 14. #5090 | C4 | semidirect |
| 15. #5084 | C4 | semidirect |
| 16. #5083 | C4 | semidirect |
| 38. #1506 | D3 | semidirect |
| 383. C3 | #9159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83354 | 2 |
| #79328 | 2 |
| C3×#1506 | 2 |
| #71821 | 2 |
| #69430 | 2 |
| #67754 | 2 |
| #67615 | 2 |
| #9159 | 3 |