Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
542 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23774608 | C2 | semidirect |
| 5. #23762001 | C2 | semidirect |
| 6. #23761911 | C2 | semidirect |
| 7. C79×#1300 | C2 | semidirect |
| 185. #1300 | D79 | semidirect |
| 186. C79 | #10097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774608 | 2 |
| #23773775 | 2 |
| #23769343 | 2 |
| #23762113 | 2 |
| #23762001 | 2 |
| #23761911 | 2 |
| C79×#1300 | 2 |
| #10097 | 79 |