Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
528 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 3. #78506 | C2 | semidirect |
| 4. #70792 | C2 | semidirect |
| 5. #70456 | C2 | semidirect |
| 7. C3×#1283 | C2 | semidirect |
| 38. #1283 | D3 | semidirect |
| 128. C3×M16 | SD16 | semidirect |
| 262. M16 | #204 | semidirect |
| 374. C3 | #10201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79269 | 2 |
| #79027 | 2 |
| #78506 | 2 |
| #70792 | 2 |
| #70456 | 2 |
| #69867 | 2 |
| C3×#1283 | 2 |
| #10201 | 3 |