Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
614 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 117 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×#5155 | C2 | semidirect |
| 3. C22×#827 | C2 | semidirect |
| 4. #72038 | C2 | semidirect |
| 5. C2×#4562 | C2 | semidirect |
| 6. C2×#4503 | C2 | semidirect |
| 7. #67804 | C2 | semidirect |
| 391. C3 | #13326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D16 | 2 |
| C2×#5155 | 2 |
| C22×#827 | 2 |
| #72038 | 2 |
| C2×#4562 | 2 |
| C2×#4503 | 2 |
| #67804 | 2 |
| #13326 | 3 |