Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
540 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 3. #89984 | C2 | semidirect |
| 4. #89983 | C2 | semidirect |
| 5. #89757 | C2 | semidirect |
| 6. #89723 | C2 | semidirect |
| 7. C4×C4⋊Dic7 | C2 | semidirect |
| 8. #89704 | C2 | semidirect |
| 11. C4×C7×D4 | C4 | semidirect |
| 84. C4×D4 | Dic7 | semidirect |
| 169. C7 | #2319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×D4 | 2 |
| #89993 | 2 |
| #89984 | 2 |
| #89983 | 2 |
| #89757 | 2 |
| #89723 | 2 |
| C4×C4⋊Dic7 | 2 |
| #89704 | 2 |
| #2319 | 7 |