Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
456 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 97 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. #23763436 | C2 | semidirect |
| 3. #23763423 | C2 | semidirect |
| 6. #23761305 | C2 | semidirect |
| 7. C79×#1305 | C2 | semidirect |
| 8. C2×#14579169 | C4 | semidirect |
| 17. #19098591 | C4 | semidirect |
| 18. #19098531 | C4 | semidirect |
| 20. #19098521 | C4 | semidirect |
| 220. #1305 | D79 | semidirect |
| 221. C79 | #8629 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772090 | 2 |
| #23763436 | 2 |
| #23763423 | 2 |
| #23761944 | 2 |
| #23761941 | 2 |
| #23761305 | 2 |
| C79×#1305 | 2 |
| #8629 | 79 |