Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
494 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 149 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×#518 | C2 | semidirect |
| 2. C22×#1142 | C2 | semidirect |
| 4. #90217 | C2 | semidirect |
| 5. #89791 | C2 | semidirect |
| 6. #89788 | C2 | semidirect |
| 7. #89776 | C2 | semidirect |
| 8. #89774 | C2 | semidirect |
| 9. #89771 | C2 | semidirect |
| 27. #6438 | C22 | semidirect |
| 28. #6432 | C22 | semidirect |
| 29. #6384 | C22 | semidirect |
| 30. #6384 | C22 | semidirect |
| 31. #6383 | C22 | semidirect |
| 32. C4⋊(C7⋊C8) | C22 | semidirect |
| 71. #518 | D7 | semidirect |
| 212. C7 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#518 | 2 |
| C22×#1142 | 2 |
| C2×#6495 | 2 |
| #90217 | 2 |
| #89791 | 2 |
| #89788 | 2 |
| #89776 | 2 |
| #89774 | 2 |
| #89771 | 2 |
| #3042 | 7 |