Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #89859 | C2 | semidirect |
| 4. #89856 | C2 | semidirect |
| 5. #89838 | C2 | semidirect |
| 6. #89838 | C2 | semidirect |
| 8. #89771 | C2 | semidirect |
| 9. #89770 | C2 | semidirect |
| 11. #89736 | C2 | semidirect |
| 14. C7×C4⋊Q8 | C22 | semidirect |
| 16. C7×#125 | C22 | semidirect |
| 33. #6382 | C22 | semidirect |
| 34. #6382 | C22 | semidirect |
| 35. #6382 | C22 | semidirect |
| 36. #6381 | C22 | semidirect |
| 37. #6381 | C22 | semidirect |
| 38. #6381 | C22 | semidirect |
| 39. C4⋊(C7⋊C8) | C22 | semidirect |
| 40. C4⋊(C7⋊C8) | C22 | semidirect |
| 48. C2×D28 | Q8 | semidirect |
| 76. #544 | D7 | semidirect |
| 117. C4⋊Q8 | C2×D7 | semidirect |
| 119. #125 | C2×D7 | semidirect |
| 225. C7 | #3081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#544 | 2 |
| #90212 | 2 |
| #89859 | 2 |
| #89856 | 2 |
| #89838 | 2 |
| #89773 | 2 |
| #89771 | 2 |
| #89770 | 2 |
| C2×#6383 | 2 |
| #89736 | 2 |
| #3081 | 7 |