Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #90315 | C2 | semidirect |
| 2. C7×#467 | C2 | semidirect |
| 3. #89963 | C2 | semidirect |
| 4. Q16×Dic7 | C2 | semidirect |
| 6. C2×C8×Dic7 | C2 | semidirect |
| 7. #89820 | C2 | semidirect |
| 8. #89650 | C2 | semidirect |
| 9. #89644 | C2 | semidirect |
| 10. #89572 | C2 | semidirect |
| 11. #89560 | C2 | semidirect |
| 76. #467 | D7 | semidirect |
| 214. C7 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90315 | 2 |
| C7×#467 | 2 |
| #89963 | 2 |
| Q16×Dic7 | 2 |
| #89887 | 2 |
| C2×C8×Dic7 | 2 |
| #89820 | 2 |
| #89650 | 2 |
| #89644 | 2 |
| #89572 | 2 |
| #89560 | 2 |
| #3168 | 7 |