Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
124 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 104. C7 | #2229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #89650 | 2 |
| #89645 | 2 |
| C7×#366 | 2 |
| #89298 | 2 |
| Dic7⋊C16 | 2 |
| #89287 | 2 |
| #89285 | 2 |
| #2229 | 7 |