Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
534 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26021236 | C2 | semidirect |
| 3. #26018784 | C2 | semidirect |
| 5. #26018158 | C2 | semidirect |
| 6. #26018104 | C2 | semidirect |
| 10. #19151909 | C4 | semidirect |
| 13. #19151736 | C4 | semidirect |
| 31. C22×Dic178 | C2×C4 | semidirect |
| 39. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 50. C22⋊#10623494 | C2×C4 | semidirect |
| 237. C89 | #9341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031058 | 2 |
| #26021236 | 2 |
| #26018784 | 2 |
| #26018768 | 2 |
| #26018158 | 2 |
| #26018104 | 2 |
| C89×#2377 | 2 |
| #9341 | 89 |