Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 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. #81934 | C2 | semidirect |
| 3. C3×#2240 | C2 | semidirect |
| 4. #71384 | C2 | semidirect |
| 5. #71291 | C2 | semidirect |
| 6. #69198 | C2 | semidirect |
| 7. #69176 | C2 | semidirect |
| 8. #69065 | C2 | semidirect |
| 9. C4×#798 | C2 | semidirect |
| 41. #2240 | D3 | semidirect |
| 148. C3⋊C16 | #41 | semidirect |
| 325. C3 | #33751 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #81934 | 2 |
| #81775 | 2 |
| C3×#2240 | 2 |
| #71384 | 2 |
| #71291 | 2 |
| #69198 | 2 |
| #69176 | 2 |
| #69065 | 2 |
| C4×#798 | 2 |
| #33751 | 3 |