Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
540 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 540 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 |
|---|---|---|
| 1. #23771386 | C2 | semidirect |
| 5. #23761526 | C2 | semidirect |
| 6. #23761526 | C2 | semidirect |
| 7. C79×#1394 | C2 | semidirect |
| 234. #1394 | D79 | semidirect |
| 235. C79 | #13379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771386 | 2 |
| #23763361 | 2 |
| #23763358 | 2 |
| #23761526 | 2 |
| C79×#1394 | 2 |
| #13379 | 79 |