Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
494 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 71 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. #23765085 | C2 | semidirect |
| 3. #23761549 | C2 | semidirect |
| 4. C79×#1525 | C2 | semidirect |
| 15. #19098360 | C22 | semidirect |
| 19. #329×C79 | C22 | semidirect |
| 176. #1525 | D79 | semidirect |
| 178. C79 | #13564 | semidirect |
| 193. #329 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772748 | 2 |
| #23765085 | 2 |
| #23761549 | 2 |
| C79×#1525 | 2 |
| #13564 | 79 |