Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
602 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 602 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 |
|---|---|---|
| 2. #26020369 | C2 | semidirect |
| 3. C2×#19151346 | C2 | semidirect |
| 5. C4×C4⋊C8×C89 | C2 | semidirect |
| 138. C4×C4⋊C8 | D89 | semidirect |
| 141. C89 | #9699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028609 | 2 |
| #26020369 | 2 |
| C2×#19151346 | 2 |
| C2×#19151341 | 2 |
| C4×C4⋊C8×C89 | 2 |
| #9699 | 89 |