Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
324 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 63 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. #23765209 | C2 | semidirect |
| 3. #23763547 | C2 | semidirect |
| 4. #23761392 | C2 | semidirect |
| 5. #23761391 | C2 | semidirect |
| 6. #23761384 | C2 | semidirect |
| 7. C79×#1339 | C2 | semidirect |
| 9. #19098960 | C4 | semidirect |
| 10. #19098938 | C4 | semidirect |
| 14. #19098675 | C4 | semidirect |
| 15. #19098674 | C4 | semidirect |
| 155. #1339 | D79 | semidirect |
| 156. C79 | #11837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774133 | 2 |
| #23765209 | 2 |
| #23763547 | 2 |
| #23761392 | 2 |
| #23761391 | 2 |
| #23761384 | 2 |
| C79×#1339 | 2 |
| #11837 | 79 |