Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
434 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 434 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 |
|---|---|---|
| 129. C3×C8 | #101 | semidirect |
| 186. C8 | #824 | semidirect |
| 202. C3 | #9808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4682 | 2 |
| C3×#1566 | 2 |
| #70522 | 2 |
| #70506 | 2 |
| #69725 | 2 |
| #9808 | 3 |