Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
564 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 181 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×Dic28 | C2 | semidirect |
| 4. C2×#6432 | C2 | semidirect |
| 5. C2×C7×#97 | C2 | semidirect |
| 6. #89487 | C2 | direct (N × H) |
| 15. C2×Dic28 | C22 | semidirect |
| 21. #6432 | C22 | semidirect |
| 22. C7×#97 | C22 | semidirect |
| 52. C2×#97 | D7 | semidirect |
| 89. #97 | C2×D7 | semidirect |
| 124. C2×C7 | #497 | semidirect |
| 149. C7 | C2×#497 | semidirect |
| 162. C2 | #89487 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic28 | 2 |
| C22×#1132 | 2 |
| C2×#6438 | 2 |
| C2×#6432 | 2 |
| C2×C7×#97 | 2 |
| #89487 | 2 |
| C2×#497 | 7 |