Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
274 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 83 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×#106 | C2 | semidirect |
| 4. #89749 | C2 | semidirect |
| 6. C2×#6381 | C2 | semidirect |
| 7. #89345 | C2 | semidirect |
| 50. C2×#106 | D7 | semidirect |
| 174. C7 | #2092 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#106 | 2 |
| C2×#6395 | 2 |
| #89760 | 2 |
| #89749 | 2 |
| C2×#6383 | 2 |
| C2×#6381 | 2 |
| #89345 | 2 |
| #2092 | 7 |