Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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. D4×Dic14 | C2 | semidirect |
| 3. #89866 | C2 | semidirect |
| 4. #89865 | C2 | semidirect |
| 5. #89813 | C2 | semidirect |
| 6. #89812 | C2 | semidirect |
| 7. #89791 | C2 | semidirect |
| 8. C4×#1142 | C2 | semidirect |
| 9. D4×C7⋊C8 | C2 | semidirect |
| 10. #89743 | C2 | semidirect |
| 11. C2×#6384 | C2 | semidirect |
| 95. C7×D4 | SD16 | semidirect |
| 114. Dic14 | #41 | semidirect |
| 216. D4 | #1142 | semidirect |
| 234. C7 | #3298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#547 | 2 |
| D4×Dic14 | 2 |
| #89866 | 2 |
| #89865 | 2 |
| #89813 | 2 |
| #89812 | 2 |
| #89791 | 2 |
| C4×#1142 | 2 |
| D4×C7⋊C8 | 2 |
| #89743 | 2 |
| C2×#6384 | 2 |
| #3298 | 7 |