Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
262 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 79 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. #89896 | C2 | semidirect |
| 5. #89696 | C2 | semidirect |
| 6. C7×#339 | C2 | semidirect |
| 7. #89328 | C2 | semidirect |
| 20. #6379 | C4 | semidirect |
| 21. #6379 | C4 | semidirect |
| 60. #339 | D7 | semidirect |
| 175. C7 | #1861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90436 | 2 |
| #89896 | 2 |
| #89777 | 2 |
| C2×#6379 | 2 |
| #89696 | 2 |
| C7×#339 | 2 |
| #89328 | 2 |
| #1861 | 7 |