Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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. C7×#544 | C2 | semidirect |
| 3. #89861 | C2 | semidirect |
| 4. #89860 | C2 | semidirect |
| 5. #89840 | C2 | semidirect |
| 6. #89839 | C2 | semidirect |
| 7. #89774 | C2 | semidirect |
| 8. #89773 | C2 | semidirect |
| 9. #89769 | C2 | semidirect |
| 10. #89738 | C2 | semidirect |
| 11. C2×#6383 | C2 | semidirect |
| 15. C7×C4⋊Q8 | C22 | semidirect |
| 17. C7×#125 | C22 | semidirect |
| 29. #6384 | C22 | semidirect |
| 30. #6384 | C22 | semidirect |
| 31. #6384 | C22 | semidirect |
| 36. #6383 | C22 | semidirect |
| 37. #6383 | C22 | semidirect |
| 38. #6383 | C22 | semidirect |
| 39. #6377 | C22 | semidirect |
| 40. C4×C7⋊C8 | C22 | semidirect |
| 78. #544 | D7 | semidirect |
| 126. C4⋊Q8 | C2×D7 | semidirect |
| 129. #125 | C2×D7 | semidirect |
| 244. C7 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#544 | 2 |
| #90216 | 2 |
| #89861 | 2 |
| #89860 | 2 |
| #89840 | 2 |
| #89839 | 2 |
| #89774 | 2 |
| #89773 | 2 |
| #89769 | 2 |
| #89738 | 2 |
| C2×#6383 | 2 |
| #3136 | 7 |