Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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. C2×C7×AGL(1,ℤ/8) | C2 | semidirect |
| 2. #90521 | C2 | semidirect |
| 3. #90489 | C2 | semidirect |
| 4. C22×#1141 | C2 | semidirect |
| 5. #90005 | C2 | semidirect |
| 6. #89937 | C2 | semidirect |
| 7. #89922 | C2 | semidirect |
| 8. #89903 | C2 | semidirect |
| 9. #89891 | C2 | semidirect |
| 14. C2×C7×SD16 | C22 | semidirect |
| 15. C2×C7×D8 | C22 | semidirect |
| 18. #6510 | C22 | semidirect |
| 19. #6503 | C22 | semidirect |
| 22. D4×Dic7 | C22 | semidirect |
| 29. #6409 | C22 | semidirect |
| 30. #6406 | C22 | semidirect |
| 31. #6395 | C22 | semidirect |
| 32. Dic7⋊C8 | C22 | semidirect |
| 42. C2×C7×D4 | D4 | semidirect |
| 68. C2×AGL(1,ℤ/8) | D7 | semidirect |
| 112. C2×SD16 | C2×D7 | semidirect |
| 115. C2×D8 | C2×D7 | semidirect |
| 161. C2×D4 | C22⋊D7 | semidirect |
| 219. C7 | #3041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×AGL(1,ℤ/8) | 2 |
| #90521 | 2 |
| #90489 | 2 |
| C22×#1141 | 2 |
| #90005 | 2 |
| #89937 | 2 |
| #89922 | 2 |
| #89903 | 2 |
| #89891 | 2 |
| #3041 | 7 |