Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
120 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 31. C7×C16 | Q8 | semidirect |
| 32. C7⋊C16 | Q8 | semidirect |
| 83. C16 | Dic14 | semidirect |
| 98. C7 | #2255 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #89650 | 2 |
| #89646 | 2 |
| C7×#367 | 2 |
| #89299 | 2 |
| #89297 | 2 |
| #89285 | 2 |
| #89284 | 2 |
| #2255 | 7 |