Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
482 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26019013 | C2 | semidirect |
| 3. #26018851 | C2 | semidirect |
| 4. #26018850 | C2 | semidirect |
| 5. #26018603 | C2 | semidirect |
| 6. #26018533 | C2 | semidirect |
| 7. C89×#1469 | C2 | semidirect |
| 208. #1469 | D89 | semidirect |
| 210. C89 | #9787 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151980 | 2 |
| #26019013 | 2 |
| #26018851 | 2 |
| #26018850 | 2 |
| #26018603 | 2 |
| #26018533 | 2 |
| C89×#1469 | 2 |
| #9787 | 89 |