Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 490 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. C7×#529 | C2 | semidirect |
| 2. C2×#6437 | C2 | semidirect |
| 3. #89839 | C2 | semidirect |
| 4. #89830 | C2 | semidirect |
| 5. #89818 | C2 | semidirect |
| 6. #89808 | C2 | semidirect |
| 7. #89799 | C2 | semidirect |
| 8. #89787 | C2 | semidirect |
| 9. #89698 | C2 | semidirect |
| 14. C7×#125 | C22 | semidirect |
| 15. C7×#124 | C22 | semidirect |
| 19. C4×C7×Q8 | C22 | semidirect |
| 21. C4×C7×D4 | C22 | semidirect |
| 24. C2×#1143 | C22 | semidirect |
| 25. C2×#1141 | C22 | semidirect |
| 31. #6383 | C22 | semidirect |
| 32. #6383 | C22 | semidirect |
| 33. C4⋊(C7⋊C8) | C22 | semidirect |
| 34. #6377 | C22 | semidirect |
| 73. #529 | D7 | semidirect |
| 121. #125 | C2×D7 | semidirect |
| 122. #124 | C2×D7 | semidirect |
| 126. C4×Q8 | C2×D7 | semidirect |
| 128. C4×D4 | C2×D7 | semidirect |
| 228. C7 | #3217 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#529 | 2 |
| C2×#6437 | 2 |
| #89839 | 2 |
| #89830 | 2 |
| #89818 | 2 |
| #89808 | 2 |
| #89799 | 2 |
| #89787 | 2 |
| #89698 | 2 |
| #3217 | 7 |