Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
330 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 155 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×#19151432 | C2 | semidirect |
| 2. C22⋊#15667918 | C2 | semidirect |
| 5. C2×#15667918 | C22 | semidirect |
| 68. C22×C89 | M64 | semidirect |
| 82. C89 | #13553 | semidirect |
| 147. C22 | #19151432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151432 | 2 |
| C22⋊#15667918 | 2 |
| C23×C16×C89 | 2 |
| #13553 | 89 |