Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
454 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 14. #4699 | C4 | semidirect |
| 16. #4682 | C4 | semidirect |
| 17. #4681 | C4 | semidirect |
| 222. C3 | #9850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78475 | 2 |
| C3×#1566 | 2 |
| #70514 | 2 |
| #70501 | 2 |
| C4×#815 | 2 |
| #9850 | 3 |