Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
814 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 219 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. C3×#3160 | C2 | semidirect |
| 2. #83343 | C2 | semidirect |
| 4. #71360 | C2 | semidirect |
| 5. #71359 | C2 | semidirect |
| 6. #71334 | C2 | semidirect |
| 7. #71332 | C2 | semidirect |
| 8. C2×C8×C3⋊C8 | C2 | semidirect |
| 33. #3160 | D3 | semidirect |
| 101. C2×C3×C8 | SD16 | semidirect |
| 170. C3⋊C8 | #135 | semidirect |
| 187. C2×C8 | #215 | semidirect |
| 246. C3 | #19596 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3160 | 2 |
| #83343 | 2 |
| #78467 | 2 |
| #71360 | 2 |
| #71359 | 2 |
| #71334 | 2 |
| #71332 | 2 |
| C2×C8×C3⋊C8 | 2 |
| #19596 | 3 |