Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
294 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 111 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×#19098397 | C2 | semidirect |
| 2. #23765184 | C2 | semidirect |
| 3. #23761587 | C2 | semidirect |
| 7. #19098397 | C22 | semidirect |
| 9. #19098391 | C22 | semidirect |
| 14. #508×C79 | C4 | semidirect |
| 16. C2×Q32×C79 | C4 | semidirect |
| 18. C2×D16×C79 | C4 | semidirect |
| 117. C79 | #13622 | semidirect |
| 121. #508 | Dic79 | semidirect |
| 123. C2×Q32 | Dic79 | semidirect |
| 125. C2×D16 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098397 | 2 |
| #23765184 | 2 |
| #23761587 | 2 |
| C2×#508×C79 | 2 |
| #13622 | 79 |