Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 125 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. #90214 | C2 | semidirect |
| 3. C7×#428 | C2 | semidirect |
| 4. #89905 | C2 | semidirect |
| 5. #89901 | C2 | semidirect |
| 6. #89774 | C2 | semidirect |
| 7. C2×#6382 | C2 | semidirect |
| 8. #89660 | C2 | semidirect |
| 9. #89657 | C2 | semidirect |
| 10. #89635 | C2 | semidirect |
| 11. #89634 | C2 | semidirect |
| 84. #428 | D7 | semidirect |
| 241. C7 | #3099 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90214 | 2 |
| #90201 | 2 |
| C7×#428 | 2 |
| #89905 | 2 |
| #89901 | 2 |
| #89774 | 2 |
| C2×#6382 | 2 |
| #89660 | 2 |
| #89657 | 2 |
| #89635 | 2 |
| #89634 | 2 |
| #3099 | 7 |