Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
278 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 1. #26033401 | C2 | semidirect |
| 2. #26022567 | C2 | semidirect |
| 3. C2×#19151435 | C2 | semidirect |
| 4. #26022373 | C2 | semidirect |
| 5. #26018435 | C2 | semidirect |
| 6. #26018395 | C2 | semidirect |
| 7. C89×#1420 | C2 | semidirect |
| 123. #1420 | D89 | semidirect |
| 126. C89 | #13670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033401 | 2 |
| #26022567 | 2 |
| C2×#19151435 | 2 |
| #26022373 | 2 |
| #26018435 | 2 |
| #26018395 | 2 |
| C89×#1420 | 2 |
| #13670 | 89 |