Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 8. #89650 | C2 | semidirect |
| 9. #89648 | C2 | semidirect |
| 10. #89630 | C2 | semidirect |
| 11. #89628 | C2 | semidirect |
| 51. C7×M16 | Q8 | semidirect |
| 79. #1136 | Q8 | semidirect |
| 171. M16 | Dic14 | semidirect |
| 227. C7 | #3166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90208 | 2 |
| C2×#6453 | 2 |
| C7×#428 | 2 |
| #89893 | 2 |
| M16×Dic7 | 2 |
| #89767 | 2 |
| #89736 | 2 |
| #89650 | 2 |
| #89648 | 2 |
| #89630 | 2 |
| #89628 | 2 |
| #3166 | 7 |