Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
528 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 528 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 |
| 4. #23764343 | C2 | semidirect |
| 5. #23762003 | C2 | semidirect |
| 7. C79×#1285 | C2 | semidirect |
| 212. #1285 | D79 | semidirect |
| 213. C79 | #10009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774608 | 2 |
| #23773500 | 2 |
| #23768561 | 2 |
| #23764343 | 2 |
| #23762003 | 2 |
| #23761842 | 2 |
| C79×#1285 | 2 |
| #10009 | 79 |