Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 414 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 |
|---|---|---|
| 2. C2×#6489 | C2 | semidirect |
| 3. C7×#407 | C2 | semidirect |
| 4. #89905 | C2 | semidirect |
| 5. #89893 | C2 | semidirect |
| 6. #89509 | C2 | semidirect |
| 7. #89495 | C2 | semidirect |
| 23. #6395 | C22 | semidirect |
| 24. #6392 | C22 | semidirect |
| 25. #6391 | C22 | semidirect |
| 26. #6390 | C22 | semidirect |
| 59. #407 | D7 | semidirect |
| 168. C7 | #3093 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90482 | 2 |
| C2×#6489 | 2 |
| C7×#407 | 2 |
| #89905 | 2 |
| #89893 | 2 |
| #89509 | 2 |
| #89495 | 2 |
| #3093 | 7 |