Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
334 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 105 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. #26021849 | C2 | semidirect |
| 5. #26018360 | C2 | semidirect |
| 6. #26018345 | C2 | semidirect |
| 7. C89×#1952 | C2 | semidirect |
| 14. #19151410 | C4 | semidirect |
| 149. #1952 | D89 | semidirect |
| 152. C89 | #13144 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151410 | 2 |
| C2×#19151398 | 2 |
| #26021849 | 2 |
| #26021162 | 2 |
| #26018360 | 2 |
| #26018345 | 2 |
| C89×#1952 | 2 |
| #13144 | 89 |