Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
600 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 600 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. #26020240 | C2 | semidirect |
| 4. #26018371 | C2 | semidirect |
| 5. C89×#1800 | C2 | semidirect |
| 7. C22×#13083551 | C4 | semidirect |
| 14. #19151470 | C4 | semidirect |
| 16. #19151453 | C4 | semidirect |
| 17. C4×C22⋊Dic89 | C4 | semidirect |
| 71. C23×D89 | C4⋊C4 | semidirect |
| 89. C22⋊Dic89 | C4⋊C4 | semidirect |
| 241. #1800 | D89 | semidirect |
| 244. C89 | #12795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022906 | 2 |
| C2×#19151386 | 2 |
| #26020240 | 2 |
| #26018371 | 2 |
| C89×#1800 | 2 |
| #12795 | 89 |