Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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. #90507 | C2 | semidirect |
| 2. C22×#1143 | C2 | semidirect |
| 4. #90212 | C2 | semidirect |
| 5. C7×#419 | C2 | semidirect |
| 6. #89891 | C2 | semidirect |
| 7. #89774 | C2 | semidirect |
| 8. #89591 | C2 | semidirect |
| 9. #89590 | C2 | semidirect |
| 15. #6510 | C22 | semidirect |
| 17. #6507 | C22 | semidirect |
| 29. C7×#103 | C22 | semidirect |
| 30. Dic7⋊C8 | C22 | semidirect |
| 31. #6384 | C22 | semidirect |
| 32. #6383 | C22 | semidirect |
| 75. #419 | D7 | semidirect |
| 127. #103 | C2×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 |
|---|---|
| #90507 | 2 |
| C22×#1143 | 2 |
| C2×#6471 | 2 |
| #90212 | 2 |
| C7×#419 | 2 |
| #89891 | 2 |
| #89774 | 2 |
| #89591 | 2 |
| #89590 | 2 |
| #3042 | 7 |