Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
756 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 135 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×#19151444 | C2 | semidirect |
| 4. #26018132 | C2 | semidirect |
| 5. C89×#1817 | C2 | semidirect |
| 9. #19151500 | C4 | semidirect |
| 10. #19151496 | C4 | semidirect |
| 171. #1817 | D89 | semidirect |
| 174. C89 | #9149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028583 | 2 |
| C2×#19151444 | 2 |
| C2×#19151333 | 2 |
| #26018132 | 2 |
| C89×#1817 | 2 |
| #9149 | 89 |