Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 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. #90516 | C2 | semidirect |
| 3. C2×#6472 | C2 | semidirect |
| 4. #90195 | C2 | semidirect |
| 5. C7×#417 | C2 | semidirect |
| 6. #89891 | C2 | semidirect |
| 7. C2×#6384 | C2 | semidirect |
| 8. #89590 | C2 | semidirect |
| 9. #89565 | C2 | semidirect |
| 10. #89559 | C2 | semidirect |
| 11. #89539 | C2 | semidirect |
| 97. #417 | D7 | semidirect |
| 267. C7 | #3046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90516 | 2 |
| C2×#6513 | 2 |
| C2×#6472 | 2 |
| #90195 | 2 |
| C7×#417 | 2 |
| #89891 | 2 |
| C2×#6384 | 2 |
| #89590 | 2 |
| #89565 | 2 |
| #89559 | 2 |
| #89539 | 2 |
| #3046 | 7 |