Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
494 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23764221 | C2 | semidirect |
| 5. #23761260 | C2 | semidirect |
| 6. #23761230 | C2 | semidirect |
| 7. C79×#1546 | C2 | semidirect |
| 10. #19098966 | C4 | semidirect |
| 11. #19098911 | C4 | semidirect |
| 185. #1546 | D79 | semidirect |
| 189. C79 | #9291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774521 | 2 |
| #23772117 | 2 |
| #23764221 | 2 |
| #23761961 | 2 |
| #23761260 | 2 |
| #23761230 | 2 |
| C79×#1546 | 2 |
| #9291 | 79 |