Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
674 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 674 conjugacy classes of subgroups — too many to draw. Only its 227 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 |
|---|---|---|
| 192. C3 | #23836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#870 | 2 |
| C3×#1744 | 2 |
| C4×#818 | 2 |
| C4×#817 | 2 |
| #68641 | 2 |
| #68634 | 2 |
| #23836 | 3 |