Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
476 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 476 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. #79271 | C2 | semidirect |
| 5. #70524 | C2 | semidirect |
| 6. #69862 | C2 | semidirect |
| 7. C3×#1299 | C2 | semidirect |
| 38. #1299 | D3 | semidirect |
| 347. C3 | #10111 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79271 | 2 |
| #79065 | 2 |
| #78528 | 2 |
| #70761 | 2 |
| #70524 | 2 |
| #69862 | 2 |
| C3×#1299 | 2 |
| #10111 | 3 |