Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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. C7×#536 | C2 | semidirect |
| 3. C22×#1144 | C2 | semidirect |
| 4. C2×#6505 | C2 | semidirect |
| 5. #90006 | C2 | semidirect |
| 6. #89822 | C2 | semidirect |
| 7. #89819 | C2 | semidirect |
| 8. #89776 | C2 | semidirect |
| 9. #89774 | C2 | semidirect |
| 87. #536 | D7 | semidirect |
| 260. C7 | #3011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6554 | 2 |
| C7×#536 | 2 |
| C22×#1144 | 2 |
| C2×#6505 | 2 |
| #90006 | 2 |
| #89822 | 2 |
| #89819 | 2 |
| #89776 | 2 |
| #89774 | 2 |
| #3011 | 7 |