Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
534 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26029968 | C2 | semidirect |
| 2. C2×#19151865 | C2 | semidirect |
| 3. C2×#19151411 | C2 | semidirect |
| 4. #26021980 | C2 | semidirect |
| 5. #26021872 | C2 | semidirect |
| 6. #26018364 | C2 | semidirect |
| 7. C2×#509×C89 | C2 | semidirect |
| 210. C2×#509 | D89 | semidirect |
| 217. C89 | #13323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029968 | 2 |
| C2×#19151865 | 2 |
| C2×#19151411 | 2 |
| #26021980 | 2 |
| #26021872 | 2 |
| #26018364 | 2 |
| C2×#509×C89 | 2 |
| #13323 | 89 |