Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
448 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 123 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×#556 | C2 | semidirect |
| 3. #89860 | C2 | semidirect |
| 4. #89859 | C2 | semidirect |
| 5. #89821 | C2 | semidirect |
| 6. #89818 | C2 | semidirect |
| 7. #89799 | C2 | semidirect |
| 8. C4×#1143 | C2 | semidirect |
| 9. #89784 | C2 | semidirect |
| 10. #89775 | C2 | semidirect |
| 11. #89773 | C2 | semidirect |
| 14. C7×C4⋊Q8 | C22 | semidirect |
| 17. C7×C22⋊Q8 | C22 | semidirect |
| 19. C4×C7×Q8 | C22 | semidirect |
| 21. C7×#117 | C22 | semidirect |
| 23. C2×#1143 | C22 | semidirect |
| 25. C2×#1136 | C22 | semidirect |
| 30. #6409 | C22 | semidirect |
| 31. C22⋊(C7⋊C8) | C22 | semidirect |
| 34. #6383 | C22 | semidirect |
| 35. #6383 | C22 | semidirect |
| 36. #6383 | C22 | semidirect |
| 37. #6382 | C22 | semidirect |
| 38. #6381 | C22 | semidirect |
| 39. C4⋊(C7⋊C8) | C22 | semidirect |
| 40. C4×C7⋊C8 | C22 | semidirect |
| 78. #556 | D7 | semidirect |
| 126. C4⋊Q8 | C2×D7 | semidirect |
| 130. C22⋊Q8 | C2×D7 | semidirect |
| 135. C4×Q8 | C2×D7 | semidirect |
| 138. #117 | C2×D7 | semidirect |
| 244. C7 | #3324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#556 | 2 |
| D4×D28 | 2 |
| #89860 | 2 |
| #89859 | 2 |
| #89821 | 2 |
| #89818 | 2 |
| #89799 | 2 |
| C4×#1143 | 2 |
| #89784 | 2 |
| #89775 | 2 |
| #89773 | 2 |
| #3324 | 7 |