Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
228 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 69 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. C2×#6396 | C2 | semidirect |
| 5. #89771 | C2 | semidirect |
| 6. #89767 | C2 | semidirect |
| 7. #89349 | C2 | semidirect |
| 171. C7 | #2063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#418 | 2 |
| C2×#6407 | 2 |
| C2×#6406 | 2 |
| C2×#6396 | 2 |
| #89771 | 2 |
| #89767 | 2 |
| #89349 | 2 |
| #2063 | 7 |