Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 16. #4455 | C4 | semidirect |
| 17. #4454 | C4 | semidirect |
| 18. #4454 | C4 | semidirect |
| 19. C8×C3⋊C8 | C4 | semidirect |
| 198. C3 | #8803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #69849 | 2 |
| C3×#1288 | 2 |
| #67754 | 2 |
| #67753 | 2 |
| #67670 | 2 |
| #67633 | 2 |
| #8803 | 3 |