Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
980 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 980 conjugacy classes of subgroups — too many to draw. Only its 135 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×#19151461 | C2 | semidirect |
| 3. C2×#19151333 | C2 | semidirect |
| 4. #26018132 | C2 | semidirect |
| 5. C89×#1779 | C2 | semidirect |
| 6. C2×#15667986 | C4 | semidirect |
| 13. #19151458 | C4 | semidirect |
| 41. #15667919 | D4 | semidirect |
| 206. #1779 | D89 | semidirect |
| 209. C89 | #9158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028534 | 2 |
| C2×#19151461 | 2 |
| C2×#19151333 | 2 |
| #26018132 | 2 |
| C89×#1779 | 2 |
| #9158 | 89 |