Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
2942 conjugacy classes of subgroups; only the 1179 normal subgroups are shown.
This group has 2942 conjugacy classes of subgroups — too many to draw. Only its 1179 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×C89⋊#401 | C2 | direct (N × H) |
| 7. C89⋊#401 | C22 | direct (N × H) |
| 57. C22×C89 | #401 | semidirect |
| 68. C2×C89 | C2×#401 | semidirect |
| 76. C89 | C22×#401 | semidirect |
| 129. C22 | C89⋊#401 | direct (N × H) |
| 139. C2 | C2×C89⋊#401 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C89⋊#401 | 2 |
| C22×#15667919 | 2 |
| C22×#95×C89 | 2 |
| C22×#401 | 89 |