Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 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. C2×#6510 | C2 | semidirect |
| 2. C2×#6505 | C2 | semidirect |
| 4. #90213 | C2 | semidirect |
| 5. C7×#419 | C2 | semidirect |
| 6. #89890 | C2 | semidirect |
| 7. #89773 | C2 | semidirect |
| 8. #89591 | C2 | semidirect |
| 9. #89570 | C2 | semidirect |
| 18. C2×#1144 | C22 | semidirect |
| 20. C2×#1143 | C22 | semidirect |
| 27. #6456 | C22 | semidirect |
| 28. #6450 | C22 | semidirect |
| 32. C7×#103 | C22 | semidirect |
| 33. Dic7⋊C8 | C22 | semidirect |
| 81. #419 | D7 | semidirect |
| 137. #103 | C2×D7 | semidirect |
| 229. C7 | #3040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6510 | 2 |
| C2×#6505 | 2 |
| C2×#6471 | 2 |
| #90213 | 2 |
| C7×#419 | 2 |
| #89890 | 2 |
| #89773 | 2 |
| #89591 | 2 |
| #89570 | 2 |
| #3040 | 7 |