Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
404 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 404 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. #90412 | C2 | semidirect |
| 3. C7×#461 | C2 | semidirect |
| 4. #89947 | C2 | semidirect |
| 5. #89935 | C2 | semidirect |
| 6. #89857 | C2 | semidirect |
| 7. C4×#1142 | C2 | semidirect |
| 8. #89620 | C2 | semidirect |
| 9. #89602 | C2 | semidirect |
| 10. #89590 | C2 | semidirect |
| 11. #89560 | C2 | semidirect |
| 83. #461 | D7 | semidirect |
| 114. Dic14 | SD16 | semidirect |
| 117. C7⋊C8 | #41 | semidirect |
| 234. C7 | #3392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90412 | 2 |
| #90244 | 2 |
| C7×#461 | 2 |
| #89947 | 2 |
| #89935 | 2 |
| #89857 | 2 |
| C4×#1142 | 2 |
| #89620 | 2 |
| #89602 | 2 |
| #89590 | 2 |
| #89560 | 2 |
| #3392 | 7 |