Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#6513 | C2 | semidirect |
| 4. #90496 | C2 | semidirect |
| 5. C22×#1141 | C2 | semidirect |
| 6. C2×#6471 | C2 | semidirect |
| 7. #89948 | C2 | semidirect |
| 8. #89940 | C2 | semidirect |
| 9. #89926 | C2 | semidirect |
| 10. #89923 | C2 | semidirect |
| 11. #89894 | C2 | semidirect |
| 17. C2×C7×SD16 | C22 | semidirect |
| 18. C2×C7×D8 | C22 | semidirect |
| 22. #6510 | C22 | semidirect |
| 23. C2×#1144 | C22 | semidirect |
| 24. C2×#1143 | C22 | semidirect |
| 25. #6503 | C22 | semidirect |
| 26. #6503 | C22 | semidirect |
| 29. #6499 | C22 | semidirect |
| 30. C2×#1142 | C22 | semidirect |
| 34. C2×#1141 | C22 | semidirect |
| 39. C2×D56 | C22 | semidirect |
| 40. C2×#1132 | C22 | semidirect |
| 41. #6389 | C22 | semidirect |
| 42. C8×Dic7 | C22 | semidirect |
| 71. C7×M16 | D4 | semidirect |
| 84. C2×C7⋊C8 | D4 | semidirect |
| 90. C2×AGL(1,ℤ/8) | D7 | semidirect |
| 150. C2×SD16 | C2×D7 | semidirect |
| 156. C2×D8 | C2×D7 | semidirect |
| 224. M16 | C22⋊D7 | semidirect |
| 280. C7 | #3155 | 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 |
| C2×#6513 | 2 |
| #90496 | 2 |
| C22×#1141 | 2 |
| C2×#6471 | 2 |
| #89948 | 2 |
| #89940 | 2 |
| #89926 | 2 |
| #89923 | 2 |
| #89894 | 2 |
| #3155 | 7 |