Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
346 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 53 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. #26031647 | C2 | semidirect |
| 2. #26022203 | C2 | semidirect |
| 3. #26021536 | C2 | semidirect |
| 4. #26018247 | C2 | semidirect |
| 5. #26018243 | C2 | semidirect |
| 6. #26018202 | C2 | semidirect |
| 178. C89 | #12175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031647 | 2 |
| #26022203 | 2 |
| #26021536 | 2 |
| #26018247 | 2 |
| #26018243 | 2 |
| #26018202 | 2 |
| C89×#2190 | 2 |
| #12175 | 89 |