Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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×#544 | C2 | semidirect |
| 3. #89865 | C2 | semidirect |
| 4. #89861 | C2 | semidirect |
| 5. #89841 | C2 | semidirect |
| 6. #89840 | C2 | semidirect |
| 7. #89776 | C2 | semidirect |
| 9. #89769 | C2 | semidirect |
| 10. C2×#6384 | C2 | semidirect |
| 78. #544 | D7 | semidirect |
| 232. C7 | #3137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#544 | 2 |
| #90217 | 2 |
| #89865 | 2 |
| #89861 | 2 |
| #89841 | 2 |
| #89840 | 2 |
| #89776 | 2 |
| #89774 | 2 |
| #89769 | 2 |
| C2×#6384 | 2 |
| #89738 | 2 |
| #3137 | 7 |