Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 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. #90210 | C2 | semidirect |
| 3. C7×#428 | C2 | semidirect |
| 5. #89891 | C2 | semidirect |
| 7. C2×#6381 | C2 | semidirect |
| 8. #89662 | C2 | semidirect |
| 9. #89647 | C2 | semidirect |
| 10. #89643 | C2 | semidirect |
| 11. #89629 | C2 | semidirect |
| 47. #1157 | Q8 | semidirect |
| 82. #428 | D7 | semidirect |
| 224. C7 | #3083 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90210 | 2 |
| #90195 | 2 |
| C7×#428 | 2 |
| #89905 | 2 |
| #89891 | 2 |
| #89774 | 2 |
| C2×#6381 | 2 |
| #89662 | 2 |
| #89647 | 2 |
| #89643 | 2 |
| #89629 | 2 |
| #3083 | 7 |