Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
142 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 55 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×#500 | C2 | semidirect |
| 4. #89285 | C2 | semidirect |
| 5. C4⋊(C7⋊C16) | C2 | semidirect |
| 27. D56 | Q8 | semidirect |
| 29. #500 | D7 | semidirect |
| 96. C7 | #2226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#500 | 2 |
| C4×D56 | 2 |
| #89286 | 2 |
| #89285 | 2 |
| C4⋊(C7⋊C16) | 2 |
| #2226 | 7 |