Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
786 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26023896 | C2 | semidirect |
| 5. #26020188 | C2 | semidirect |
| 6. #26018825 | C2 | semidirect |
| 7. C89×#1282 | C2 | semidirect |
| 141. C22⋊C4×C89 | SD16 | semidirect |
| 238. #1282 | D89 | semidirect |
| 239. C89 | #9949 | semidirect |
| 373. C22⋊C4 | #13083563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031010 | 2 |
| C2×#19151739 | 2 |
| #26023896 | 2 |
| #26021088 | 2 |
| #26020188 | 2 |
| #26018825 | 2 |
| C89×#1282 | 2 |
| #9949 | 89 |