Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
508 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 107 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×#4894 | C2 | semidirect |
| 3. C2×C3×#361 | C2 | semidirect |
| 4. #72039 | C2 | semidirect |
| 5. C2×#4518 | C2 | semidirect |
| 6. #67811 | C2 | semidirect |
| 7. #67730 | C2 | semidirect |
| 16. C2×#827 | C4 | semidirect |
| 19. C2×#826 | C4 | semidirect |
| 30. C2×#361 | D3 | semidirect |
| 135. Dic12 | C22⋊C4 | semidirect |
| 137. D24 | C22⋊C4 | semidirect |
| 348. C3 | #13040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5147 | 2 |
| C2×#4894 | 2 |
| C2×C3×#361 | 2 |
| #72039 | 2 |
| C2×#4518 | 2 |
| #67811 | 2 |
| #67730 | 2 |
| #13040 | 3 |