Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
816 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26021066 | C2 | semidirect |
| 3. C2×#19151340 | C2 | semidirect |
| 4. C2×#19151337 | C2 | semidirect |
| 5. C89×#1992 | C2 | semidirect |
| 8. #19152346 | C4 | semidirect |
| 156. #1992 | D89 | semidirect |
| 160. C89 | #8508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152346 | 2 |
| #26021066 | 2 |
| C2×#19151340 | 2 |
| C2×#19151337 | 2 |
| C89×#1992 | 2 |
| #8508 | 89 |