Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 1. C7×#559 | C2 | semidirect |
| 2. #90276 | C2 | semidirect |
| 3. #89847 | C2 | semidirect |
| 5. #89831 | C2 | semidirect |
| 6. #89829 | C2 | semidirect |
| 7. C4×#1144 | C2 | semidirect |
| 8. #89799 | C2 | semidirect |
| 9. Q8×C7⋊C8 | C2 | semidirect |
| 10. #89788 | C2 | semidirect |
| 11. C4×#1141 | C2 | semidirect |
| 78. #559 | D7 | semidirect |
| 232. C7 | #3396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#559 | 2 |
| #90276 | 2 |
| #89847 | 2 |
| #89845 | 2 |
| #89831 | 2 |
| #89829 | 2 |
| C4×#1144 | 2 |
| #89799 | 2 |
| Q8×C7⋊C8 | 2 |
| #89788 | 2 |
| C4×#1141 | 2 |
| #3396 | 7 |