Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
726 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 135 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. #26020018 | C2 | semidirect |
| 2. #26018872 | C2 | semidirect |
| 3. #26018712 | C2 | semidirect |
| 4. #26018586 | C2 | semidirect |
| 6. #19151655 | C22 | semidirect |
| 8. C2×#15667923 | C22 | semidirect |
| 9. C2×C4×#10623494 | C22 | semidirect |
| 237. C89 | #8348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020018 | 2 |
| #26018872 | 2 |
| #26018712 | 2 |
| #26018586 | 2 |
| C89×#3491 | 2 |
| #8348 | 89 |