Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
866 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 866 conjugacy classes of subgroups — too many to draw. Only its 267 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 |
|---|---|---|
| 1. C2×#19151996 | C2 | semidirect |
| 3. C2×#19151949 | C2 | semidirect |
| 5. #26019853 | C2 | direct (N × H) |
| 6. C2×C82×C89 | C2 | semidirect |
| 12. #19151996 | C22 | semidirect |
| 16. #19151949 | C22 | semidirect |
| 24. C82×C89 | C22 | semidirect |
| 122. C2×C89 | #1708 | semidirect |
| 131. C2×C82 | D89 | semidirect |
| 132. C89 | C2×#1708 | semidirect |
| 150. C82 | C2×D89 | semidirect |
| 248. C2 | #26019853 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151996 | 2 |
| C2×#19151971 | 2 |
| C2×#19151949 | 2 |
| C2×#19151945 | 2 |
| #26019853 | 2 |
| C2×C82×C89 | 2 |
| C2×#1708 | 89 |