Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
240 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. C7×#559 | C2 | semidirect |
| 3. #89799 | C2 | semidirect |
| 4. #89339 | C2 | semidirect |
| 5. Q8⋊(C7⋊C8) | C2 | semidirect |
| 34. #559 | D7 | semidirect |
| 114. C7 | #1620 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#559 | 2 |
| #89845 | 2 |
| #89799 | 2 |
| #89339 | 2 |
| Q8⋊(C7⋊C8) | 2 |
| #1620 | 7 |