Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
576 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26023409 | C2 | semidirect |
| 3. #26021088 | C2 | semidirect |
| 4. #26018782 | C2 | semidirect |
| 5. #26018157 | C2 | semidirect |
| 6. #26018105 | C2 | semidirect |
| 7. C89×#1507 | C2 | semidirect |
| 10. #19151914 | C4 | semidirect |
| 13. #19151731 | C4 | semidirect |
| 31. C22×D356 | C2×C4 | semidirect |
| 42. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 57. C22⋊#10623494 | C2×C4 | semidirect |
| 253. #1507 | 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 |
| #26023409 | 2 |
| #26021088 | 2 |
| #26018782 | 2 |
| #26018157 | 2 |
| #26018105 | 2 |
| C89×#1507 | 2 |
| #9343 | 89 |