Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
402 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 85 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. #79317 | C2 | semidirect |
| 4. #69566 | C2 | semidirect |
| 6. C3×#1288 | C2 | semidirect |
| 7. #67670 | C2 | semidirect |
| 21. #4694 | C4 | semidirect |
| 22. #4693 | C4 | semidirect |
| 23. #4682 | C4 | semidirect |
| 24. #4681 | C4 | semidirect |
| 34. #1288 | D3 | semidirect |
| 305. C3 | #9418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79317 | 2 |
| #78533 | 2 |
| #70811 | 2 |
| #69566 | 2 |
| #69564 | 2 |
| C3×#1288 | 2 |
| #67670 | 2 |
| #9418 | 3 |