Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
356 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23764173 | C2 | semidirect |
| 5. #23761690 | C2 | semidirect |
| 6. #23761241 | C2 | semidirect |
| 7. C79×#1303 | C2 | semidirect |
| 16. #19098308 | C4 | semidirect |
| 17. #19098308 | C4 | semidirect |
| 18. #19098306 | C4 | semidirect |
| 19. #19098306 | C4 | semidirect |
| 175. #1303 | D79 | semidirect |
| 177. C79 | #9592 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764318 | 2 |
| #23764173 | 2 |
| #23762047 | 2 |
| #23761850 | 2 |
| #23761690 | 2 |
| #23761241 | 2 |
| C79×#1303 | 2 |
| #9592 | 79 |