Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
576 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 576 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. #26021087 | C2 | semidirect |
| 3. #26018780 | C2 | semidirect |
| 4. #26018768 | C2 | semidirect |
| 5. #26018158 | C2 | semidirect |
| 6. #26018104 | C2 | semidirect |
| 7. C89×#2377 | C2 | semidirect |
| 10. #19151914 | C4 | semidirect |
| 13. #19151731 | C4 | semidirect |
| 31. C22×D356 | C2×C4 | semidirect |
| 40. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 52. C22⋊#10623494 | C2×C4 | semidirect |
| 250. #2377 | D89 | semidirect |
| 256. C89 | #9343 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031049 | 2 |
| #26021087 | 2 |
| #26018780 | 2 |
| #26018768 | 2 |
| #26018158 | 2 |
| #26018104 | 2 |
| C89×#2377 | 2 |
| #9343 | 89 |