Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×C7×#137 | C2 | semidirect |
| 2. #41×Dic7 | C2 | semidirect |
| 4. C2×#6510 | C2 | semidirect |
| 5. #89997 | C2 | semidirect |
| 6. #89957 | C2 | semidirect |
| 7. #89937 | C2 | semidirect |
| 8. #89903 | C2 | semidirect |
| 9. #89890 | C2 | semidirect |
| 14. C2×C7×Q16 | C22 | semidirect |
| 15. C2×C7×SD16 | C22 | semidirect |
| 21. Q8×Dic7 | C22 | semidirect |
| 24. D4×Dic7 | C22 | semidirect |
| 32. #6409 | C22 | semidirect |
| 34. Dic7⋊C8 | C22 | semidirect |
| 74. C2×#137 | D7 | semidirect |
| 119. C2×Q16 | C2×D7 | semidirect |
| 121. C2×SD16 | 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×C7×#137 | 2 |
| #41×Dic7 | 2 |
| C2×#6512 | 2 |
| C2×#6510 | 2 |
| #89997 | 2 |
| #89957 | 2 |
| #89937 | 2 |
| #89903 | 2 |
| #89890 | 2 |
| #3040 | 7 |