Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
182 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 117. C3 | #13720 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #69066 | 2 |
| #69044 | 2 |
| C3×C4×C32 | 2 |
| #67597 | 2 |
| #13720 | 3 |