Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
290 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. C2×#19151428 | C2 | semidirect |
| 3. #26018446 | C2 | semidirect |
| 4. #26018443 | C2 | semidirect |
| 5. C2×M64×C89 | C2 | semidirect |
| 114. C2×M64 | D89 | semidirect |
| 118. C89 | #13625 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152030 | 2 |
| C2×#19151428 | 2 |
| #26018446 | 2 |
| #26018443 | 2 |
| C2×M64×C89 | 2 |
| #13625 | 89 |