Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
142 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 113. C3 | #7097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #68065 | 2 |
| C3×#1370 | 2 |
| #67440 | 2 |
| #7097 | 3 |