Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
130 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 32. Dic28 | Q8 | semidirect |
| 106. C7 | #2227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #89646 | 2 |
| #89645 | 2 |
| C7×#366 | 2 |
| #89298 | 2 |
| Dic7⋊C16 | 2 |
| #89287 | 2 |
| #89284 | 2 |
| #2227 | 7 |