Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
958 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 187 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×#19151968 | C2 | semidirect |
| 2. C2×#19151957 | C2 | semidirect |
| 3. #26019575 | C2 | direct (N × H) |
| 4. C2×#19151340 | C2 | semidirect |
| 5. C2×#19151338 | C2 | semidirect |
| 9. #19151968 | C22 | semidirect |
| 11. #19151957 | C22 | semidirect |
| 17. #19151340 | C22 | semidirect |
| 18. #19151338 | C22 | semidirect |
| 146. C2×C89 | #1662 | semidirect |
| 155. C89 | C2×#1662 | semidirect |
| 294. C2 | #26019575 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151968 | 2 |
| C2×#19151957 | 2 |
| #26019575 | 2 |
| C2×#19151340 | 2 |
| C2×#19151338 | 2 |
| C2×#562×C89 | 2 |
| C2×#1662 | 89 |