Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
502 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26021025 | C2 | semidirect |
| 3. #26018930 | C2 | semidirect |
| 4. C2×#19151342 | C2 | semidirect |
| 5. #26018652 | C2 | semidirect |
| 6. #26018101 | C2 | semidirect |
| 7. C89×#1545 | C2 | semidirect |
| 203. #1545 | D89 | semidirect |
| 207. C89 | #10549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030702 | 2 |
| #26021025 | 2 |
| #26018930 | 2 |
| C2×#19151342 | 2 |
| #26018652 | 2 |
| #26018101 | 2 |
| C89×#1545 | 2 |
| #10549 | 89 |