Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
464 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 95 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. #79315 | C2 | semidirect |
| 5. #70802 | C2 | semidirect |
| 6. C3×#1290 | C2 | semidirect |
| 7. #67706 | C2 | semidirect |
| 39. #1290 | D3 | semidirect |
| 412. C3 | #9244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79315 | 2 |
| C2×#4845 | 2 |
| #70828 | 2 |
| #70804 | 2 |
| #70802 | 2 |
| C3×#1290 | 2 |
| #67706 | 2 |
| #9244 | 3 |