Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
532 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 532 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 |
|---|---|---|
| 1. C2×D7×Q16 | C2 | semidirect |
| 2. C2×#6478 | C2 | semidirect |
| 4. #90366 | C2 | semidirect |
| 5. C7×#495 | C2 | semidirect |
| 6. #89953 | C2 | semidirect |
| 7. #89939 | C2 | semidirect |
| 8. #89927 | C2 | semidirect |
| 9. #89832 | C2 | semidirect |
| 10. #89471 | C2 | semidirect |
| 11. #89461 | C2 | semidirect |
| 85. #495 | D7 | semidirect |
| 225. C7 | #3156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D7×Q16 | 2 |
| C2×#6478 | 2 |
| C2×#6475 | 2 |
| #90366 | 2 |
| C7×#495 | 2 |
| #89953 | 2 |
| #89939 | 2 |
| #89927 | 2 |
| #89832 | 2 |
| #89471 | 2 |
| #89461 | 2 |
| #3156 | 7 |