Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 2. C2×#6451 | C2 | semidirect |
| 3. C7×#428 | C2 | semidirect |
| 5. #89890 | C2 | semidirect |
| 6. #89767 | C2 | semidirect |
| 8. #89662 | C2 | semidirect |
| 9. #89647 | C2 | semidirect |
| 10. #89642 | C2 | semidirect |
| 11. #89626 | C2 | semidirect |
| 51. #1157 | Q8 | semidirect |
| 91. #428 | D7 | semidirect |
| 116. D28 | C2×Q8 | semidirect |
| 123. Dic14 | C2×Q8 | semidirect |
| 252. C7 | #3079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90213 | 2 |
| C2×#6451 | 2 |
| C7×#428 | 2 |
| #89905 | 2 |
| #89890 | 2 |
| #89767 | 2 |
| #89738 | 2 |
| #89662 | 2 |
| #89647 | 2 |
| #89642 | 2 |
| #89626 | 2 |
| #3079 | 7 |