Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
726 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 211 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×C3×C82 | C2 | semidirect |
| 3. #69772 | C2 | semidirect |
| 4. #69765 | C2 | semidirect |
| 14. #4695 | C4 | semidirect |
| 19. C2×C82 | D3 | semidirect |
| 65. C2×C3×C8 | D8 | semidirect |
| 113. C3×C8 | #102 | semidirect |
| 131. C2×C8 | D24 | semidirect |
| 174. C8 | #821 | semidirect |
| 196. C3 | #9824 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4695 | 2 |
| C2×C3×C82 | 2 |
| #69772 | 2 |
| #69765 | 2 |
| #9824 | 3 |