Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
608 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 3. #26020533 | C2 | semidirect |
| 4. #26020462 | C2 | semidirect |
| 5. #26018376 | C2 | semidirect |
| 6. #26018369 | C2 | semidirect |
| 20. #19151385 | C4 | semidirect |
| 104. C24×C89 | C4⋊C4 | semidirect |
| 136. C22⋊C4×C89 | C4⋊C4 | semidirect |
| 266. C89 | #12960 | semidirect |
| 338. C24 | #13083553 | semidirect |
| 393. C22⋊C4 | #13083553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023393 | 2 |
| C2×#19151385 | 2 |
| #26020533 | 2 |
| #26020462 | 2 |
| #26018376 | 2 |
| #26018369 | 2 |
| C89×#1889 | 2 |
| #12960 | 89 |