Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
510 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23763179 | C2 | semidirect |
| 4. #23761285 | C2 | semidirect |
| 5. C79×#1298 | C2 | semidirect |
| 6. C2×#14579169 | C4 | semidirect |
| 11. #19098591 | C4 | semidirect |
| 12. #19098531 | C4 | semidirect |
| 13. #19098521 | C4 | semidirect |
| 17. #19098301 | C4 | semidirect |
| 18. #19098298 | C4 | semidirect |
| 147. #1298 | D79 | semidirect |
| 149. C79 | #8239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772090 | 2 |
| #23763179 | 2 |
| #23761892 | 2 |
| #23761285 | 2 |
| C79×#1298 | 2 |
| #8239 | 79 |