Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
470 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26018272 | C2 | semidirect |
| 4. #26018251 | C2 | semidirect |
| 6. C2×C4×Dic178 | C4 | semidirect |
| 9. #19151523 | C4 | semidirect |
| 12. #19151510 | C4 | semidirect |
| 16. #19151444 | C4 | semidirect |
| 184. C89 | #11728 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023536 | 2 |
| #26018570 | 2 |
| #26018272 | 2 |
| #26018251 | 2 |
| C4×#99×C89 | 2 |
| #11728 | 89 |