Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
438 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23771762 | C2 | semidirect |
| 4. #23761259 | C2 | semidirect |
| 5. #23761258 | C2 | semidirect |
| 6. #23761232 | C2 | semidirect |
| 178. C79 | #10364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771762 | 2 |
| #23764229 | 2 |
| #23761960 | 2 |
| #23761259 | 2 |
| #23761258 | 2 |
| #23761232 | 2 |
| C79×#1517 | 2 |
| #10364 | 79 |