Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
972 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 972 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 1. #430×D89 | C2 | semidirect |
| 3. #26021769 | C2 | semidirect |
| 4. #26021768 | C2 | semidirect |
| 5. #26021767 | C2 | semidirect |
| 6. #338×D89 | C2 | semidirect |
| 7. C89×#2091 | C2 | semidirect |
| 159. #2091 | D89 | semidirect |
| 161. C89 | #23723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #430×D89 | 2 |
| #26028695 | 2 |
| #26021769 | 2 |
| #26021768 | 2 |
| #26021767 | 2 |
| #338×D89 | 2 |
| C89×#2091 | 2 |
| #23723 | 89 |