Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
538 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 538 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 |
|---|---|---|
| 3. #26020351 | C2 | semidirect |
| 5. #26018160 | C2 | semidirect |
| 6. #26018104 | C2 | semidirect |
| 7. C89×#1820 | C2 | semidirect |
| 10. #19151916 | C4 | semidirect |
| 11. #19151911 | C4 | semidirect |
| 57. C22⋊#10623494 | C2×C4 | semidirect |
| 66. C2×C4⋊C4×C89 | C2×C4 | semidirect |
| 67. C2×C4⋊C4×C89 | C2×C4 | semidirect |
| 235. #1820 | D89 | semidirect |
| 239. C89 | #9525 | semidirect |
| 279. C2×C4⋊C4 | C4×D89 | semidirect |
| 280. C2×C4⋊C4 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030192 | 2 |
| #26023014 | 2 |
| #26020351 | 2 |
| #26018780 | 2 |
| #26018160 | 2 |
| #26018104 | 2 |
| C89×#1820 | 2 |
| #9525 | 89 |