Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
364 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 73 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. #23761389 | C2 | semidirect |
| 5. #23761388 | C2 | semidirect |
| 6. #23761387 | C2 | semidirect |
| 7. C79×#1340 | C2 | semidirect |
| 8. C2×Q16×D79 | C4 | semidirect |
| 12. #19098822 | C4 | semidirect |
| 14. #19098818 | C4 | semidirect |
| 18. #19098598 | C4 | semidirect |
| 184. #1340 | D79 | semidirect |
| 185. C79 | #11869 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773053 | 2 |
| #23765019 | 2 |
| #23763445 | 2 |
| #23761389 | 2 |
| #23761388 | 2 |
| #23761387 | 2 |
| C79×#1340 | 2 |
| #11869 | 79 |