Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
390 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 2. #23765165 | C2 | semidirect |
| 5. #23763525 | C2 | semidirect |
| 6. #23761507 | C2 | semidirect |
| 7. C79×#1383 | C2 | semidirect |
| 11. #19098674 | C4 | semidirect |
| 12. #19098669 | C4 | semidirect |
| 157. #1383 | D79 | semidirect |
| 158. C79 | #12828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772283 | 2 |
| #23765165 | 2 |
| #23765137 | 2 |
| #23765127 | 2 |
| #23763525 | 2 |
| #23761507 | 2 |
| C79×#1383 | 2 |
| #12828 | 79 |