Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
914 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 914 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×#19152003 | C2 | semidirect |
| 2. C2×#19151978 | C2 | semidirect |
| 5. #26019923 | C2 | direct (N × H) |
| 6. C2×#322×C89 | C2 | semidirect |
| 13. #19152003 | C22 | semidirect |
| 15. #19151978 | C22 | semidirect |
| 24. #322×C89 | C22 | semidirect |
| 124. C2×C89 | #1722 | semidirect |
| 133. C2×#322 | D89 | semidirect |
| 134. C89 | C2×#1722 | semidirect |
| 152. #322 | C2×D89 | semidirect |
| 252. C2 | #26019923 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152003 | 2 |
| C2×#19151978 | 2 |
| C2×#19151971 | 2 |
| C2×#19151945 | 2 |
| #26019923 | 2 |
| C2×#322×C89 | 2 |
| C2×#1722 | 89 |