Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
400 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 248. C3 | #9725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78475 | 2 |
| C3×C4×#108 | 2 |
| #69862 | 2 |
| #69856 | 2 |
| C8×#208 | 2 |
| #9725 | 3 |