Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
326 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26018443 | C2 | direct (N × H) |
| 4. C2×M64×C89 | C2 | semidirect |
| 14. #19151428 | C22 | semidirect |
| 17. M64×C89 | C22 | semidirect |
| 101. C2×C89 | #1419 | semidirect |
| 105. C2×M64 | D89 | semidirect |
| 108. C89 | C2×#1419 | semidirect |
| 119. M64 | C2×D89 | semidirect |
| 205. C2 | #26018443 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1424 | 2 |
| C2×#19151428 | 2 |
| #26018443 | 2 |
| C2×M64×C89 | 2 |
| C2×#1419 | 89 |