Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
5990 conjugacy classes of subgroups; only the 699 normal subgroups are shown.
This group has 5990 conjugacy classes of subgroups — too many to draw. Only its 699 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×#19151562 | C2 | semidirect |
| 2. #26020162 | C2 | semidirect |
| 4. C22×#13083558 | C22 | semidirect |
| 6. C2×C22⋊#10623494 | C22 | semidirect |
| 14. C22×#10623494 | C23 | semidirect |
| 41. C24×C89 | M16 | semidirect |
| 91. C22×C89 | #407 | semidirect |
| 105. C89 | #20579 | semidirect |
| 141. C24 | #13083558 | semidirect |
| 193. C22 | #19151562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151562 | 2 |
| #26020162 | 2 |
| C25×C4×C89 | 2 |
| #20579 | 89 |