Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
484 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 83 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. #83222 | C2 | semidirect |
| 4. C3×#1556 | C2 | semidirect |
| 6. #70813 | C2 | semidirect |
| 7. #67751 | C2 | semidirect |
| 35. #1556 | D3 | semidirect |
| 345. C3 | #10137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83222 | 2 |
| C2×#5089 | 2 |
| #79351 | 2 |
| C3×#1556 | 2 |
| #70828 | 2 |
| #70813 | 2 |
| #67751 | 2 |
| #10137 | 3 |