Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
384 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. C7×#491 | C2 | semidirect |
| 4. #89854 | C2 | semidirect |
| 5. #89841 | C2 | semidirect |
| 7. #89569 | C2 | semidirect |
| 9. #89475 | C2 | semidirect |
| 62. #491 | D7 | direct (N × H) |
| 141. D7 | #491 | direct (N × H) |
| 160. C7 | C2×#491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D7×C4⋊Q8 | 2 |
| D7×#125 | 2 |
| C7×#491 | 2 |
| #89854 | 2 |
| #89841 | 2 |
| D7×#103 | 2 |
| #89569 | 2 |
| D7×#97 | 2 |
| #89475 | 2 |
| C2×#491 | 7 |