Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
356 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#19151422 | C2 | semidirect |
| 5. #26018357 | C2 | semidirect |
| 6. #26018332 | C2 | semidirect |
| 7. C89×#1773 | C2 | semidirect |
| 16. #19151398 | C4 | semidirect |
| 142. #1773 | D89 | semidirect |
| 145. C89 | #13142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151422 | 2 |
| C2×#19151410 | 2 |
| #26021967 | 2 |
| #26021128 | 2 |
| #26018357 | 2 |
| #26018332 | 2 |
| C89×#1773 | 2 |
| #13142 | 89 |