Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
274 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 94. C3×C8 | Q32 | semidirect |
| 131. C8 | Dic24 | semidirect |
| 143. C3 | #12528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #69066 | 2 |
| #69065 | 2 |
| #68065 | 2 |
| #68063 | 2 |
| C3×#1312 | 2 |
| #12528 | 3 |