Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
496 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 79 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×#19151395 | C2 | semidirect |
| 2. #26018876 | C2 | semidirect |
| 3. #26018400 | C2 | semidirect |
| 8. #19151395 | C22 | semidirect |
| 10. #19151338 | C22 | semidirect |
| 182. C89 | #13565 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151395 | 2 |
| #26018876 | 2 |
| #26018400 | 2 |
| C2×#455×C89 | 2 |
| #13565 | 89 |