Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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. #90270 | C2 | semidirect |
| 3. C4×C7×SD16 | C2 | semidirect |
| 4. #89941 | C2 | semidirect |
| 5. #89799 | C2 | semidirect |
| 6. #89780 | C2 | semidirect |
| 7. #89635 | C2 | semidirect |
| 8. #89579 | C2 | semidirect |
| 9. D7×#102 | C2 | semidirect |
| 10. #89466 | C2 | semidirect |
| 11. C8×D28 | C2 | semidirect |
| 15. C4×C7×Q8 | C22 | semidirect |
| 17. #6509 | C22 | semidirect |
| 18. C2×#1143 | C22 | semidirect |
| 20. C2×C8×D7 | C22 | semidirect |
| 23. D7×C4⋊C4 | C22 | semidirect |
| 29. #6432 | C22 | semidirect |
| 30. C7×#106 | C22 | semidirect |
| 31. C7×#103 | C22 | semidirect |
| 33. C4×C7×C8 | C22 | semidirect |
| 35. #6395 | C22 | semidirect |
| 36. #6395 | C22 | semidirect |
| 37. (C2×D7)⋊C8 | C22 | semidirect |
| 38. #6383 | C22 | semidirect |
| 39. #6382 | C22 | semidirect |
| 40. C4⋊(C7⋊C8) | C22 | semidirect |
| 86. C4×SD16 | D7 | semidirect |
| 114. D28 | SD16 | semidirect |
| 135. C4×Q8 | C2×D7 | semidirect |
| 141. #106 | C2×D7 | semidirect |
| 143. #103 | C2×D7 | semidirect |
| 150. C4×C8 | C2×D7 | semidirect |
| 246. C7 | #3295 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90270 | 2 |
| D4×D28 | 2 |
| C4×C7×SD16 | 2 |
| #89941 | 2 |
| #89799 | 2 |
| #89780 | 2 |
| #89635 | 2 |
| #89579 | 2 |
| D7×#102 | 2 |
| #89466 | 2 |
| C8×D28 | 2 |
| #3295 | 7 |