Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
454 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 9. #19151977 | C4 | semidirect |
| 10. #19151950 | C4 | semidirect |
| 102. C42×C89 | Q16 | semidirect |
| 173. C89 | #9297 | semidirect |
| 268. C42 | #13083564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031197 | 2 |
| #26023000 | 2 |
| #26018934 | 2 |
| #26018816 | 2 |
| #26018112 | 2 |
| #26018081 | 2 |
| C89×#1995 | 2 |
| #9297 | 89 |