Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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. #90208 | C2 | semidirect |
| 5. #89892 | C2 | semidirect |
| 6. M16×Dic7 | C2 | semidirect |
| 7. #89776 | C2 | semidirect |
| 8. #89540 | C2 | semidirect |
| 9. #89537 | C2 | semidirect |
| 21. #6453 | C22 | semidirect |
| 22. #6451 | C22 | semidirect |
| 27. #6390 | C22 | semidirect |
| 28. #6389 | C22 | semidirect |
| 29. C8×Dic7 | C22 | semidirect |
| 30. #6384 | C22 | semidirect |
| 190. C7 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6499 | 2 |
| #90208 | 2 |
| C7×#418 | 2 |
| #89987 | 2 |
| #89892 | 2 |
| M16×Dic7 | 2 |
| #89776 | 2 |
| #89540 | 2 |
| #89537 | 2 |
| #3140 | 7 |