Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
476 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 3. #78506 | C2 | semidirect |
| 5. #69879 | C2 | semidirect |
| 6. #69856 | C2 | semidirect |
| 7. #67669 | C2 | semidirect |
| 347. C3 | #10118 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83321 | 2 |
| #83270 | 2 |
| #78506 | 2 |
| C3×#1525 | 2 |
| #69879 | 2 |
| #69856 | 2 |
| #67669 | 2 |
| #10118 | 3 |