Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1054 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1054 conjugacy classes of subgroups — too many to draw. Only its 167 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. #26021047 | C2 | semidirect |
| 2. #26020244 | C2 | semidirect |
| 3. #26018929 | C2 | semidirect |
| 4. #26018703 | C2 | semidirect |
| 6. #19151622 | C22 | semidirect |
| 7. C2×C4⋊#10623494 | C22 | semidirect |
| 10. C2×C4×#10623494 | C22 | semidirect |
| 197. C89 | #8353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021047 | 2 |
| #26020244 | 2 |
| #26018929 | 2 |
| #26018703 | 2 |
| C89×#3496 | 2 |
| #8353 | 89 |