Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
430 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. #23762117 | C2 | semidirect |
| 5. #23761270 | C2 | semidirect |
| 6. #23761256 | C2 | semidirect |
| 7. C79×#1987 | C2 | semidirect |
| 9. #19098955 | C4 | semidirect |
| 10. #19098931 | C4 | semidirect |
| 192. #1987 | D79 | semidirect |
| 197. C79 | #9376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774427 | 2 |
| #23772536 | 2 |
| #23762117 | 2 |
| #23761923 | 2 |
| #23761270 | 2 |
| #23761256 | 2 |
| C79×#1987 | 2 |
| #9376 | 79 |