Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
1168 conjugacy classes of subgroups; only the 541 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 541 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×#125 | C2 | semidirect |
| 2. #90379 | C2 | direct (N × H) |
| 5. C2×#6451 | C2 | semidirect |
| 6. C2×#6450 | C2 | semidirect |
| 8. C2×#6433 | C2 | semidirect |
| 12. C7×#125 | C22 | semidirect |
| 25. #6451 | C22 | semidirect |
| 26. #6450 | C22 | semidirect |
| 28. #6433 | C22 | semidirect |
| 38. C2×C4×D7 | Q8 | semidirect |
| 56. C2×#125 | D7 | semidirect |
| 78. C4×D7 | C2×Q8 | semidirect |
| 85. #125 | C2×D7 | semidirect |
| 135. C2×C7 | #533 | semidirect |
| 158. C7 | C2×#533 | semidirect |
| 172. C2 | #90379 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#125 | 2 |
| #90379 | 2 |
| C2×#6459 | 2 |
| C2×#6455 | 2 |
| C2×#6451 | 2 |
| C2×#6450 | 2 |
| C2×C42×D7 | 2 |
| C2×#6433 | 2 |
| C2×#533 | 7 |