Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
548 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 2. #73645 | C2 | semidirect |
| 3. C3×#1502 | C2 | semidirect |
| 4. #71814 | C2 | semidirect |
| 5. #70756 | C2 | semidirect |
| 6. #67738 | C2 | semidirect |
| 7. #67620 | C2 | semidirect |
| 15. #5083 | C4 | semidirect |
| 16. #5072 | C4 | semidirect |
| 33. #1502 | D3 | semidirect |
| 411. C3 | #9181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83297 | 2 |
| #73645 | 2 |
| C3×#1502 | 2 |
| #71814 | 2 |
| #70756 | 2 |
| #67738 | 2 |
| #67620 | 2 |
| #9181 | 3 |