Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
520 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 520 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×#525 | C2 | semidirect |
| 2. C2×#6513 | C2 | semidirect |
| 3. #90482 | C2 | semidirect |
| 4. C23×C7⋊C8 | C2 | semidirect |
| 5. #90005 | C2 | semidirect |
| 6. #89823 | C2 | semidirect |
| 7. #89820 | C2 | semidirect |
| 8. #89813 | C2 | semidirect |
| 9. #89810 | C2 | semidirect |
| 10. #89774 | C2 | semidirect |
| 11. #89770 | C2 | semidirect |
| 23. C2×#1144 | C22 | semidirect |
| 24. C2×#1143 | C22 | semidirect |
| 25. C2×#1142 | C22 | semidirect |
| 26. C2×#1141 | C22 | semidirect |
| 37. #6409 | C22 | semidirect |
| 38. #6406 | C22 | semidirect |
| 39. #6384 | C22 | semidirect |
| 40. #6383 | C22 | semidirect |
| 41. #6382 | C22 | semidirect |
| 42. #6381 | C22 | semidirect |
| 84. C2×C7⋊C8 | D4 | semidirect |
| 91. #525 | D7 | semidirect |
| 173. C22×C7 | #135 | semidirect |
| 271. C7 | #3050 | semidirect |
| 281. C22 | #6513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#525 | 2 |
| C2×#6513 | 2 |
| #90482 | 2 |
| C23×C7⋊C8 | 2 |
| #90005 | 2 |
| #89823 | 2 |
| #89820 | 2 |
| #89813 | 2 |
| #89810 | 2 |
| #89774 | 2 |
| #89770 | 2 |
| #3050 | 7 |