Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
488 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 488 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×#125 | C2 | semidirect |
| 3. #89839 | C2 | direct (N × H) |
| 4. C2×#6383 | C2 | semidirect |
| 5. C2×#6377 | C2 | semidirect |
| 9. C7×#125 | C22 | semidirect |
| 16. #6383 | C22 | semidirect |
| 17. #6377 | C22 | semidirect |
| 36. C2×#125 | D7 | semidirect |
| 61. #125 | C2×D7 | semidirect |
| 93. C2×C7 | #490 | semidirect |
| 112. C7 | C2×#490 | semidirect |
| 124. C2 | #89839 | 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 |
| C2×#6437 | 2 |
| #89839 | 2 |
| C2×#6383 | 2 |
| C2×#6377 | 2 |
| C2×#490 | 7 |