Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×C7×Q16 | C2 | semidirect |
| 3. C2×D7×Q16 | C2 | semidirect |
| 4. #90000 | C2 | semidirect |
| 5. #89960 | C2 | semidirect |
| 6. #89958 | C2 | semidirect |
| 7. Q16×Dic7 | C2 | semidirect |
| 8. #89954 | C2 | semidirect |
| 9. #89953 | C2 | semidirect |
| 10. #89888 | C2 | semidirect |
| 58. C7×Q16 | D4 | semidirect |
| 82. C22×Q16 | D7 | semidirect |
| 106. C22⋊D7 | Q16 | direct (N × H) |
| 153. C22×C7 | C2×Q16 | semidirect |
| 157. C2×D7 | C2×Q16 | semidirect |
| 167. Dic7 | C2×Q16 | semidirect |
| 187. Q16 | C22⋊D7 | direct (N × H) |
| 242. C7 | D4×Q16 | semidirect |
| 248. C22 | D7×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×Q16 | 2 |
| Q8×C22⋊D7 | 2 |
| C2×D7×Q16 | 2 |
| #90000 | 2 |
| #89960 | 2 |
| #89958 | 2 |
| Q16×Dic7 | 2 |
| #89954 | 2 |
| #89953 | 2 |
| #89888 | 2 |
| C8×C22⋊D7 | 2 |
| D4×Q16 | 7 |