Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
340 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 123 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×#557 | C2 | semidirect |
| 5. #89854 | C2 | semidirect |
| 6. #89853 | C2 | semidirect |
| 9. #89796 | C2 | semidirect |
| 10. #89794 | C2 | semidirect |
| 11. #89793 | C2 | semidirect |
| 74. #557 | D7 | semidirect |
| 213. C7 | #3372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#557 | 2 |
| #90270 | 2 |
| #89855 | 2 |
| #89854 | 2 |
| #89853 | 2 |
| #89798 | 2 |
| C4×#1143 | 2 |
| #89796 | 2 |
| #89794 | 2 |
| #89793 | 2 |
| #3372 | 7 |