Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 485 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. #90388 | C2 | direct (N × H) |
| 5. C2×#6453 | C2 | semidirect |
| 6. C2×#6450 | C2 | semidirect |
| 8. C2×#6432 | C2 | semidirect |
| 11. C7×#125 | C22 | semidirect |
| 25. #6453 | C22 | semidirect |
| 26. #6450 | C22 | semidirect |
| 28. #6432 | C22 | semidirect |
| 56. C2×#125 | D7 | semidirect |
| 83. #125 | C2×D7 | semidirect |
| 132. C2×C7 | #541 | semidirect |
| 154. C7 | C2×#541 | semidirect |
| 168. C2 | #90388 | 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 |
| #90388 | 2 |
| C2×#6461 | 2 |
| C2×#6460 | 2 |
| C2×#6453 | 2 |
| C2×#6450 | 2 |
| C2×#6435 | 2 |
| C2×#6432 | 2 |
| C2×#541 | 7 |