Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
488 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 488 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. #90419 | C2 | semidirect |
| 3. C7×#486 | C2 | semidirect |
| 4. #89860 | C2 | semidirect |
| 5. #89848 | C2 | semidirect |
| 6. #89548 | C2 | semidirect |
| 7. #89534 | C2 | semidirect |
| 8. #89465 | C2 | semidirect |
| 9. #89457 | C2 | semidirect |
| 13. C7×C4⋊Q8 | C22 | semidirect |
| 20. C2×#1142 | C22 | semidirect |
| 21. C2×#1132 | C22 | semidirect |
| 25. #6450 | C22 | semidirect |
| 28. #6432 | C22 | semidirect |
| 29. C7×#102 | C22 | semidirect |
| 30. C4×C7×C8 | C22 | semidirect |
| 32. Dic7⋊C8 | C22 | semidirect |
| 33. #6383 | C22 | semidirect |
| 34. C4×C7⋊C8 | C22 | semidirect |
| 75. #486 | D7 | semidirect |
| 105. C4×D7 | SD16 | semidirect |
| 115. C4⋊Q8 | C2×D7 | semidirect |
| 130. #102 | C2×D7 | semidirect |
| 133. C4×C8 | C2×D7 | semidirect |
| 223. C7 | #3208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90419 | 2 |
| D7×#127 | 2 |
| C7×#486 | 2 |
| #89860 | 2 |
| #89848 | 2 |
| #89548 | 2 |
| #89534 | 2 |
| #89465 | 2 |
| #89457 | 2 |
| #3208 | 7 |