Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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×#554 | C2 | semidirect |
| 3. #89860 | C2 | semidirect |
| 4. #89856 | C2 | semidirect |
| 5. #89820 | C2 | semidirect |
| 6. #89818 | C2 | semidirect |
| 7. #89799 | C2 | semidirect |
| 8. C4×#1143 | C2 | semidirect |
| 9. D4×C7⋊C8 | C2 | semidirect |
| 10. #89740 | C2 | semidirect |
| 11. C2×#6383 | C2 | semidirect |
| 14. C7×C4⋊Q8 | C22 | semidirect |
| 17. C7×C22⋊Q8 | C22 | semidirect |
| 18. C4×C7×Q8 | C22 | semidirect |
| 21. C2×C7×C4⋊C4 | C22 | semidirect |
| 23. C2×#1143 | C22 | semidirect |
| 25. C22×C7⋊C8 | 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. #6382 | C22 | semidirect |
| 39. C4⋊(C7⋊C8) | C22 | semidirect |
| 40. C4×C7⋊C8 | C22 | semidirect |
| 78. #554 | D7 | semidirect |
| 98. C7×D4 | SD16 | semidirect |
| 127. C4⋊Q8 | C2×D7 | semidirect |
| 131. C22⋊Q8 | C2×D7 | semidirect |
| 135. C4×Q8 | C2×D7 | semidirect |
| 139. C2×C4⋊C4 | C2×D7 | semidirect |
| 230. D4 | #1143 | semidirect |
| 246. C7 | #3295 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#554 | 2 |
| D4×D28 | 2 |
| #89860 | 2 |
| #89856 | 2 |
| #89820 | 2 |
| #89818 | 2 |
| #89799 | 2 |
| C4×#1143 | 2 |
| D4×C7⋊C8 | 2 |
| #89740 | 2 |
| C2×#6383 | 2 |
| #3295 | 7 |