Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
426 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 178. C3×C8 | #101 | semidirect |
| 254. C8 | #824 | semidirect |
| 272. C3 | #9794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4680 | 2 |
| C3×#1566 | 2 |
| #70524 | 2 |
| #70522 | 2 |
| #70508 | 2 |
| #70506 | 2 |
| C8×#208 | 2 |
| #9794 | 3 |