Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
412 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23761413 | C2 | semidirect |
| 5. #23761412 | C2 | semidirect |
| 6. #23761411 | C2 | semidirect |
| 7. C79×#1348 | C2 | semidirect |
| 8. C2×Q16×D79 | C4 | semidirect |
| 12. #19098805 | C4 | semidirect |
| 16. #19098801 | C4 | semidirect |
| 17. #107×D79 | C4 | semidirect |
| 192. #1348 | D79 | semidirect |
| 193. C79 | #11889 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #467×D79 | 2 |
| #23765009 | 2 |
| #23763424 | 2 |
| #23761413 | 2 |
| #23761412 | 2 |
| #23761411 | 2 |
| C79×#1348 | 2 |
| #11889 | 79 |