Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
460 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 109 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. #23763203 | C2 | semidirect |
| 5. #23763202 | C2 | semidirect |
| 6. #23761529 | C2 | semidirect |
| 7. C79×#1395 | C2 | semidirect |
| 8. C2×#14579169 | C4 | semidirect |
| 15. #19098586 | C4 | semidirect |
| 18. #19098529 | C4 | semidirect |
| 21. C2×C8×Dic79 | C4 | semidirect |
| 22. #19098361 | C4 | semidirect |
| 23. #19098359 | C4 | semidirect |
| 212. #1395 | D79 | semidirect |
| 213. C79 | #12633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772108 | 2 |
| #23765083 | 2 |
| #23765063 | 2 |
| #23763203 | 2 |
| #23763202 | 2 |
| #23761529 | 2 |
| C79×#1395 | 2 |
| #12633 | 79 |