Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
378 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26022046 | C2 | semidirect |
| 3. C2×#19151428 | C2 | semidirect |
| 6. #26018368 | C2 | semidirect |
| 7. C89×#1382 | C2 | semidirect |
| 19. #19151381 | C4 | semidirect |
| 144. #1382 | D89 | semidirect |
| 145. C89 | #12927 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028860 | 2 |
| #26022046 | 2 |
| C2×#19151428 | 2 |
| C2×#19151381 | 2 |
| #26020303 | 2 |
| #26018368 | 2 |
| C89×#1382 | 2 |
| #12927 | 89 |