Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1164 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1164 conjugacy classes of subgroups — too many to draw. Only its 271 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. #26021428 | C2 | semidirect |
| 3. #26019984 | C2 | semidirect |
| 4. C89×#3458 | C2 | semidirect |
| 19. C22×Dic178 | Q8 | semidirect |
| 20. C22×D356 | Q8 | semidirect |
| 22. C22×C4×D89 | Q8 | semidirect |
| 133. #3458 | D89 | semidirect |
| 137. C89 | #23474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151571 | 2 |
| #26021428 | 2 |
| #26019984 | 2 |
| C89×#3458 | 2 |
| #23474 | 89 |