Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
646 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 646 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23771864 | C2 | semidirect |
| 3. #23765071 | C2 | semidirect |
| 4. #23765051 | C2 | semidirect |
| 5. #23761530 | C2 | semidirect |
| 6. #23761520 | C2 | semidirect |
| 7. C79×#1796 | C2 | semidirect |
| 8. C2×#14579186 | C4 | semidirect |
| 9. C22×#11929611 | C4 | semidirect |
| 16. #19098572 | C4 | semidirect |
| 17. #19098559 | C4 | semidirect |
| 252. #1796 | D79 | semidirect |
| 255. C79 | #13103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772686 | 2 |
| #23771864 | 2 |
| #23765071 | 2 |
| #23765051 | 2 |
| #23761530 | 2 |
| #23761520 | 2 |
| C79×#1796 | 2 |
| #13103 | 79 |