Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
460 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 460 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 |
| 4. #89997 | C2 | semidirect |
| 5. #89961 | C2 | semidirect |
| 6. #89960 | C2 | semidirect |
| 7. #89878 | C2 | semidirect |
| 53. C22×Q16 | D7 | semidirect |
| 161. C7 | #3059 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×Q16 | 2 |
| #90507 | 2 |
| C2×#6464 | 2 |
| #89997 | 2 |
| #89961 | 2 |
| #89960 | 2 |
| #89878 | 2 |
| #3059 | 7 |