Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
428 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 91 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. C2×#4509 | C2 | semidirect |
| 3. C2×#4508 | C2 | semidirect |
| 4. #70721 | C2 | semidirect |
| 5. C2×#4495 | C2 | semidirect |
| 6. #70649 | C2 | semidirect |
| 7. C3×#1382 | C2 | semidirect |
| 34. #1382 | D3 | semidirect |
| 72. #812 | D4 | semidirect |
| 359. C3 | #13387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79183 | 2 |
| C2×#4509 | 2 |
| C2×#4508 | 2 |
| #70721 | 2 |
| C2×#4495 | 2 |
| #70649 | 2 |
| C3×#1382 | 2 |
| #13387 | 3 |