Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
808 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 808 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26020244 | C2 | semidirect |
| 4. #26018369 | C2 | semidirect |
| 5. C89×#1799 | C2 | semidirect |
| 6. C23×C4×D89 | C4 | semidirect |
| 13. #19151470 | C4 | semidirect |
| 15. #19151453 | C4 | semidirect |
| 17. C4×C22⋊Dic89 | C4 | semidirect |
| 73. C23×D89 | C4⋊C4 | semidirect |
| 101. C22⋊Dic89 | C4⋊C4 | semidirect |
| 242. C4×C89 | AΣL(1,𝔽16) | semidirect |
| 260. #1799 | D89 | semidirect |
| 262. C89 | #12793 | semidirect |
| 502. C4 | #19151384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667980 | 2 |
| C2×#19151384 | 2 |
| #26020244 | 2 |
| #26018369 | 2 |
| C89×#1799 | 2 |
| #12793 | 89 |