Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
384 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 115 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. #90404 | C2 | semidirect |
| 2. #90276 | C2 | semidirect |
| 3. C7×#460 | C2 | semidirect |
| 4. #89940 | C2 | semidirect |
| 5. #89937 | C2 | semidirect |
| 7. C4×#1144 | C2 | semidirect |
| 8. #89620 | C2 | semidirect |
| 9. #89602 | C2 | semidirect |
| 10. #89559 | C2 | semidirect |
| 11. #89528 | C2 | semidirect |
| 84. #460 | D7 | semidirect |
| 232. C7 | #3396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90404 | 2 |
| #90276 | 2 |
| C7×#460 | 2 |
| #89940 | 2 |
| #89937 | 2 |
| #89845 | 2 |
| C4×#1144 | 2 |
| #89620 | 2 |
| #89602 | 2 |
| #89559 | 2 |
| #89528 | 2 |
| #3396 | 7 |