Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
376 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 376 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 |
|---|---|---|
| 4. #23761516 | C2 | semidirect |
| 5. #23761500 | C2 | semidirect |
| 6. #23761499 | C2 | semidirect |
| 7. C79×#1389 | C2 | semidirect |
| 154. #1389 | D79 | semidirect |
| 157. C79 | #12874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771992 | 2 |
| #23765020 | 2 |
| #23763447 | 2 |
| #23761516 | 2 |
| #23761500 | 2 |
| #23761499 | 2 |
| C79×#1389 | 2 |
| #12874 | 79 |