Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1998 conjugacy classes of subgroups; only the 491 normal subgroups are shown.
This group has 1998 conjugacy classes of subgroups — too many to draw. Only its 491 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 |
|---|---|---|
| 2. #26018520 | C2 | semidirect |
| 12. C22×C4⋊C4×C89 | C4 | semidirect |
| 107. C89 | #14342 | semidirect |
| 111. C22×C4⋊C4 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151461 | 2 |
| #26018520 | 2 |
| #26018475 | 2 |
| C23×C4⋊C4×C89 | 2 |
| #14342 | 89 |