Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
420 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 4. #70786 | C2 | semidirect |
| 5. #70749 | C2 | semidirect |
| 6. #69559 | C2 | semidirect |
| 7. #67631 | C2 | semidirect |
| 356. C3 | #10467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83314 | 2 |
| C3×#1517 | 2 |
| #71804 | 2 |
| #70786 | 2 |
| #70749 | 2 |
| #69559 | 2 |
| #67631 | 2 |
| #10467 | 3 |