Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
558 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 199 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 |
|---|---|---|
| 13. #4699 | C4 | semidirect |
| 68. C2×C3⋊C8 | Q16 | semidirect |
| 173. C3 | #9825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4699 | 2 |
| C3×#1845 | 2 |
| C2×C8×C3⋊C8 | 2 |
| #69582 | 2 |
| #9825 | 3 |