Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
190 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 3. #26018458 | C2 | direct (N × H) |
| 12. M64×C89 | C4 | semidirect |
| 14. C2×C32×C89 | C4 | semidirect |
| 28. C32×C89 | C2×C4 | semidirect |
| 72. C2×C89 | #1426 | semidirect |
| 78. C89 | C2×#1426 | semidirect |
| 82. M64 | Dic89 | semidirect |
| 84. C2×C32 | Dic89 | semidirect |
| 102. C32 | C2×Dic89 | semidirect |
| 145. C2 | #26018458 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151428 | 2 |
| C2×#19151426 | 2 |
| #26018458 | 2 |
| C2×M64×C89 | 2 |
| C2×#1426 | 89 |