Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
140 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 4. #89299 | C2 | semidirect |
| 5. #89298 | C2 | semidirect |
| 96. C7 | #2236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #89888 | 2 |
| C2×#6392 | 2 |
| C7×C22⋊C16 | 2 |
| #89299 | 2 |
| #89298 | 2 |
| #2236 | 7 |