Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 2. #90191 | C2 | semidirect |
| 5. #89894 | C2 | semidirect |
| 6. #89892 | C2 | semidirect |
| 7. C2×#6384 | C2 | semidirect |
| 8. #89569 | C2 | semidirect |
| 9. #89564 | C2 | semidirect |
| 10. #89540 | C2 | semidirect |
| 11. #89537 | C2 | semidirect |
| 232. C7 | #3137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90516 | 2 |
| #90191 | 2 |
| C7×#417 | 2 |
| #90005 | 2 |
| #89894 | 2 |
| #89892 | 2 |
| C2×#6384 | 2 |
| #89569 | 2 |
| #89564 | 2 |
| #89540 | 2 |
| #89537 | 2 |
| #3137 | 7 |