Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
416 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23763688 | C2 | semidirect |
| 5. #23763619 | C2 | semidirect |
| 6. #23761522 | C2 | semidirect |
| 7. C79×#1395 | C2 | semidirect |
| 195. #1395 | D79 | semidirect |
| 197. C79 | #12963 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772458 | 2 |
| #23765039 | 2 |
| #23763816 | 2 |
| #23763688 | 2 |
| #23763619 | 2 |
| #23761522 | 2 |
| C79×#1395 | 2 |
| #12963 | 79 |