Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
570 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 570 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. #83317 | C2 | semidirect |
| 3. #83271 | C2 | semidirect |
| 4. #71814 | C2 | semidirect |
| 5. #71814 | C2 | semidirect |
| 6. #69828 | C2 | semidirect |
| 7. #67661 | C2 | semidirect |
| 138. C2×C3×C8 | SD16 | semidirect |
| 277. C2×C8 | #214 | semidirect |
| 383. C3 | #10221 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3150 | 2 |
| #83317 | 2 |
| #83271 | 2 |
| #71814 | 2 |
| #69828 | 2 |
| #67661 | 2 |
| #10221 | 3 |