Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
732 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 165 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×C7×2−1+4 | C2 | semidirect |
| 2. #90521 | C2 | semidirect |
| 3. C2×#6512 | C2 | semidirect |
| 4. C22×#1143 | C2 | semidirect |
| 5. #90010 | C2 | semidirect |
| 6. #90006 | C2 | semidirect |
| 7. #90005 | C2 | semidirect |
| 8. #89999 | C2 | semidirect |
| 9. #89997 | C2 | semidirect |
| 16. C2×C7×#41 | C22 | semidirect |
| 19. C22×C7×Q8 | C22 | semidirect |
| 33. #6409 | C22 | semidirect |
| 34. #6409 | C22 | semidirect |
| 35. #6406 | C22 | semidirect |
| 36. C22⋊(C7⋊C8) | C22 | semidirect |
| 46. C7×#41 | D4 | semidirect |
| 54. C2×C7×Q8 | D4 | semidirect |
| 84. C2×2−1+4 | D7 | semidirect |
| 138. C2×#41 | C2×D7 | semidirect |
| 141. C22×Q8 | C2×D7 | semidirect |
| 184. #41 | C22⋊D7 | semidirect |
| 192. C2×Q8 | C22⋊D7 | semidirect |
| 267. C7 | #3010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×2−1+4 | 2 |
| #90521 | 2 |
| C2×#6512 | 2 |
| C22×#1143 | 2 |
| #90010 | 2 |
| #90006 | 2 |
| #90005 | 2 |
| #89999 | 2 |
| #89997 | 2 |
| #3010 | 7 |