Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
650 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#19151929 | C2 | semidirect |
| 4. #26021237 | C2 | semidirect |
| 5. #26020339 | C2 | semidirect |
| 7. C89×#1282 | C2 | semidirect |
| 130. C22⋊C4×C89 | SD16 | semidirect |
| 221. #1282 | D89 | semidirect |
| 222. C89 | #9960 | semidirect |
| 345. C22⋊C4 | #13083563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031010 | 2 |
| C2×#19151929 | 2 |
| #26024723 | 2 |
| #26021237 | 2 |
| #26020339 | 2 |
| #26018821 | 2 |
| C89×#1282 | 2 |
| #9960 | 89 |