Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
316 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 3. #23765652 | C2 | semidirect |
| 4. #23763016 | C2 | semidirect |
| 6. #23761316 | C2 | semidirect |
| 7. C79×#2247 | C2 | semidirect |
| 99. #2247 | D79 | semidirect |
| 103. C79 | #12520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765657 | 2 |
| #23765656 | 2 |
| #23765652 | 2 |
| #23763016 | 2 |
| #23763007 | 2 |
| #23761316 | 2 |
| C79×#2247 | 2 |
| #12520 | 79 |