Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
144 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 81 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. #89289 | C2 | semidirect |
| 12. #6386 | C4 | semidirect |
| 14. C2×C7⋊C16 | C4 | semidirect |
| 97. C7 | #2155 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#108 | 2 |
| #89878 | 2 |
| C2×#6386 | 2 |
| #89289 | 2 |
| #2155 | 7 |