Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#535 | C2 | semidirect |
| 2. #90524 | C2 | semidirect |
| 3. C2×#6511 | C2 | semidirect |
| 4. C2×#6495 | C2 | semidirect |
| 5. C2×#6406 | C2 | semidirect |
| 6. #89814 | C2 | semidirect |
| 7. #89813 | C2 | semidirect |
| 8. #89811 | C2 | semidirect |
| 9. #89810 | C2 | semidirect |
| 10. #89774 | C2 | semidirect |
| 11. #89767 | C2 | semidirect |
| 28. #6493 | C22 | semidirect |
| 30. #6487 | C22 | semidirect |
| 32. C2×#1136 | C22 | semidirect |
| 34. C22×C7⋊C8 | C22 | semidirect |
| 37. #6384 | C22 | semidirect |
| 38. #6384 | C22 | semidirect |
| 39. #6383 | C22 | semidirect |
| 40. #6383 | C22 | semidirect |
| 41. #6382 | C22 | semidirect |
| 42. #6381 | C22 | semidirect |
| 80. #1136 | D4 | semidirect |
| 89. #535 | D7 | semidirect |
| 273. C7 | #3062 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#535 | 2 |
| #90524 | 2 |
| C2×#6511 | 2 |
| C2×#6495 | 2 |
| C2×#6406 | 2 |
| #89814 | 2 |
| #89813 | 2 |
| #89811 | 2 |
| #89810 | 2 |
| #89774 | 2 |
| #89767 | 2 |
| #3062 | 7 |