Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
478 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 4. C2×#19151335 | C2 | semidirect |
| 5. #26018139 | C2 | semidirect |
| 6. #26018094 | C2 | semidirect |
| 7. C89×#1472 | C2 | semidirect |
| 10. #19151928 | C4 | semidirect |
| 11. #19151911 | C4 | semidirect |
| 15. #19151754 | C4 | semidirect |
| 16. #19151737 | C4 | semidirect |
| 238. #1472 | D89 | semidirect |
| 241. C89 | #9263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031033 | 2 |
| #26029306 | 2 |
| #26018757 | 2 |
| C2×#19151335 | 2 |
| #26018139 | 2 |
| #26018094 | 2 |
| C89×#1472 | 2 |
| #9263 | 89 |