Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
504 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 504 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 |
|---|---|---|
| 2. #26029306 | C2 | semidirect |
| 3. #26018754 | C2 | semidirect |
| 4. C2×#19151331 | C2 | semidirect |
| 5. #26018611 | C2 | semidirect |
| 6. #26018140 | C2 | semidirect |
| 7. C89×#1280 | C2 | semidirect |
| 10. #19151934 | C4 | semidirect |
| 12. #19151917 | C4 | semidirect |
| 15. #19151751 | C4 | semidirect |
| 17. #19151734 | C4 | semidirect |
| 252. #1280 | D89 | semidirect |
| 253. C89 | #9264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031019 | 2 |
| #26029306 | 2 |
| #26018754 | 2 |
| C2×#19151331 | 2 |
| #26018611 | 2 |
| #26018140 | 2 |
| C89×#1280 | 2 |
| #9264 | 89 |