Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
908 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 4. #69963 | C2 | semidirect |
| 5. #67675 | C2 | semidirect |
| 19. #4947 | C4 | semidirect |
| 36. C22×Dic6 | C2×C4 | semidirect |
| 56. C3⋊#95 | C2×C4 | semidirect |
| 172. C23×C3 | #103 | semidirect |
| 308. C23 | #816 | semidirect |
| 386. C3 | #9013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4947 | 2 |
| #82094 | 2 |
| C2×C3×#323 | 2 |
| #69963 | 2 |
| #67675 | 2 |
| #9013 | 3 |