Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
218 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 201. C3 | #12423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C8×Q16 | 2 |
| #70916 | 2 |
| #70910 | 2 |
| #68063 | 2 |
| #67475 | 2 |
| #67474 | 2 |
| #67439 | 2 |
| #12423 | 3 |