Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
750 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 750 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #26018854 | C2 | semidirect |
| 4. #26018700 | C2 | semidirect |
| 5. #26018698 | C2 | semidirect |
| 7. C89×#1528 | C2 | semidirect |
| 251. #1528 | D89 | semidirect |
| 255. C89 | #8371 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152286 | 2 |
| C4×#15667928 | 2 |
| #26018854 | 2 |
| #26018700 | 2 |
| #26018698 | 2 |
| #26018592 | 2 |
| C89×#1528 | 2 |
| #8371 | 89 |