Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
840 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 840 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 |
|---|---|---|
| 2. C2×#19151384 | C2 | semidirect |
| 3. C4×#15667929 | C2 | semidirect |
| 4. C89×#1799 | C2 | semidirect |
| 5. C23×D356 | C4 | semidirect |
| 13. #19151458 | C4 | semidirect |
| 14. #19151453 | C4 | semidirect |
| 38. #15667929 | D4 | semidirect |
| 196. C4×C89 | AΣL(1,𝔽16) | semidirect |
| 210. #1799 | D89 | semidirect |
| 212. C89 | #13218 | semidirect |
| 405. C4 | #19151384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023608 | 2 |
| C2×#19151384 | 2 |
| C4×#15667929 | 2 |
| C89×#1799 | 2 |
| #13218 | 89 |