Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
608 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #26020462 | C2 | semidirect |
| 5. #26018376 | C2 | semidirect |
| 6. #26018370 | C2 | semidirect |
| 7. C89×#1867 | C2 | semidirect |
| 20. #19151384 | C4 | semidirect |
| 79. C23×D89 | C4⋊C4 | semidirect |
| 98. C22⋊Dic89 | C4⋊C4 | semidirect |
| 262. #1867 | D89 | semidirect |
| 266. C89 | #12960 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023390 | 2 |
| C2×#19151384 | 2 |
| #26020660 | 2 |
| #26020462 | 2 |
| #26018376 | 2 |
| #26018370 | 2 |
| C89×#1867 | 2 |
| #12960 | 89 |