Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
546 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 99 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. #83317 | C2 | semidirect |
| 3. #78528 | C2 | semidirect |
| 4. C3×#1980 | C2 | semidirect |
| 5. #69489 | C2 | semidirect |
| 6. #69469 | C2 | semidirect |
| 7. #67668 | C2 | semidirect |
| 36. #1980 | D3 | semidirect |
| 389. C3 | #10196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83317 | 2 |
| #83310 | 2 |
| #78528 | 2 |
| C3×#1980 | 2 |
| #69489 | 2 |
| #69469 | 2 |
| #67668 | 2 |
| #10196 | 3 |