Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
218 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 87. Dic12 | Q16 | semidirect |
| 197. C3 | #12446 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #71389 | 2 |
| #71362 | 2 |
| #69295 | 2 |
| #68557 | 2 |
| C3×#1364 | 2 |
| #67555 | 2 |
| #67475 | 2 |
| #12446 | 3 |