Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
508 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23766581 | C2 | semidirect |
| 2. #23762126 | C2 | semidirect |
| 4. #23761265 | C2 | semidirect |
| 16. #494×C79 | C4 | semidirect |
| 17. #492×C79 | C4 | semidirect |
| 122. C79 | #9429 | semidirect |
| 127. #494 | Dic79 | semidirect |
| 128. #492 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766581 | 2 |
| #23762126 | 2 |
| #23761947 | 2 |
| #23761265 | 2 |
| C79×#3152 | 2 |
| #9429 | 79 |