Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
398 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 89 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. #70777 | C2 | semidirect |
| 6. C3×#1302 | C2 | semidirect |
| 7. #67662 | C2 | semidirect |
| 34. #1302 | D3 | semidirect |
| 291. C3 | #9008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79317 | 2 |
| #78497 | 2 |
| #70801 | 2 |
| #70777 | 2 |
| #70765 | 2 |
| C3×#1302 | 2 |
| #67662 | 2 |
| #9008 | 3 |