Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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. #90419 | C2 | semidirect |
| 3. C7×#489 | C2 | semidirect |
| 4. #89861 | C2 | semidirect |
| 5. #89827 | C2 | semidirect |
| 6. #89576 | C2 | semidirect |
| 7. #89569 | C2 | semidirect |
| 8. #89544 | C2 | semidirect |
| 9. #89536 | C2 | semidirect |
| 10. #89486 | C2 | semidirect |
| 11. D7×#97 | C2 | semidirect |
| 89. #489 | D7 | semidirect |
| 248. C7 | #3135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90419 | 2 |
| #90359 | 2 |
| C7×#489 | 2 |
| #89861 | 2 |
| #89827 | 2 |
| #89576 | 2 |
| #89569 | 2 |
| #89544 | 2 |
| #89536 | 2 |
| #89486 | 2 |
| D7×#97 | 2 |
| #3135 | 7 |