Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
786 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26023892 | C2 | semidirect |
| 5. #26018823 | C2 | semidirect |
| 6. #26018099 | C2 | semidirect |
| 7. C89×#1787 | C2 | semidirect |
| 109. C22⋊Dic89 | SD16 | semidirect |
| 236. #1787 | D89 | semidirect |
| 239. C89 | #9949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031010 | 2 |
| C2×#19151737 | 2 |
| #26023892 | 2 |
| #26021087 | 2 |
| #26018823 | 2 |
| #26018099 | 2 |
| C89×#1787 | 2 |
| #9949 | 89 |