Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
408 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 408 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 |
|---|---|---|
| 2. C2×#19151422 | C2 | semidirect |
| 3. C2×#19151421 | C2 | semidirect |
| 6. #26018360 | C2 | semidirect |
| 7. C89×#1387 | C2 | semidirect |
| 19. #19151379 | C4 | semidirect |
| 159. #1387 | D89 | semidirect |
| 160. C89 | #12931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151645 | 2 |
| C2×#19151422 | 2 |
| C2×#19151421 | 2 |
| C2×#19151379 | 2 |
| #26020286 | 2 |
| #26018360 | 2 |
| C89×#1387 | 2 |
| #12931 | 89 |