Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
532 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 532 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. #26021236 | C2 | semidirect |
| 5. #26020673 | C2 | semidirect |
| 6. #26020429 | C2 | semidirect |
| 7. C89×#1289 | C2 | semidirect |
| 119. C22⋊Dic89 | SD16 | semidirect |
| 257. #1289 | D89 | semidirect |
| 258. C89 | #10565 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031010 | 2 |
| #26021236 | 2 |
| #26021087 | 2 |
| #26020678 | 2 |
| #26020673 | 2 |
| #26020429 | 2 |
| C89×#1289 | 2 |
| #10565 | 89 |