Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#6489 | C2 | semidirect |
| 3. #89987 | C2 | semidirect |
| 4. #89979 | C2 | semidirect |
| 5. #89807 | C2 | semidirect |
| 6. #89806 | C2 | semidirect |
| 7. #89805 | C2 | semidirect |
| 8. #89736 | C2 | semidirect |
| 22. #6489 | C22 | semidirect |
| 23. C2×C4⋊Dic7 | C22 | semidirect |
| 24. C2×C4⋊Dic7 | C22 | semidirect |
| 27. #6406 | C22 | semidirect |
| 28. #6406 | C22 | semidirect |
| 29. C22⋊(C7⋊C8) | C22 | semidirect |
| 30. C22⋊(C7⋊C8) | C22 | semidirect |
| 31. #6382 | C22 | semidirect |
| 32. #6381 | C22 | semidirect |
| 221. C7 | #3094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#121 | 2 |
| C2×#6489 | 2 |
| #89987 | 2 |
| #89979 | 2 |
| #89807 | 2 |
| #89806 | 2 |
| #89805 | 2 |
| #89736 | 2 |
| #3094 | 7 |