Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
662 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 255 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 |
|---|---|---|
| 22. #4702 | C4 | semidirect |
| 49. #815 | Q8 | semidirect |
| 187. C3 | #21737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79044 | 2 |
| #78479 | 2 |
| C3×#1849 | 2 |
| #70704 | 2 |
| #70703 | 2 |
| #70515 | 2 |
| #69804 | 2 |
| #21737 | 3 |