Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26022046 | C2 | semidirect |
| 3. #26021999 | C2 | semidirect |
| 4. C2×#19151407 | C2 | semidirect |
| 5. #26021873 | C2 | semidirect |
| 6. #26018350 | C2 | semidirect |
| 7. C89×#1815 | C2 | semidirect |
| 182. #1815 | D89 | semidirect |
| 184. C89 | #13391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029972 | 2 |
| #26022046 | 2 |
| #26021999 | 2 |
| C2×#19151407 | 2 |
| #26021873 | 2 |
| #26018350 | 2 |
| C89×#1815 | 2 |
| #13391 | 89 |