Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
392 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 133 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. #89841 | C2 | semidirect |
| 4. #89840 | C2 | semidirect |
| 5. #89839 | C2 | semidirect |
| 6. #89738 | C2 | semidirect |
| 7. C4×#1136 | C2 | semidirect |
| 47. C2×#125 | D7 | semidirect |
| 139. C7 | #3142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#125 | 2 |
| #90168 | 2 |
| #89841 | 2 |
| #89840 | 2 |
| #89839 | 2 |
| #89738 | 2 |
| C4×#1136 | 2 |
| #3142 | 7 |