Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
544 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 544 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. #23761847 | C2 | semidirect |
| 5. #23761266 | C2 | semidirect |
| 6. #23761265 | C2 | semidirect |
| 7. C79×#1491 | C2 | semidirect |
| 211. #1491 | D79 | semidirect |
| 215. C79 | #9491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771817 | 2 |
| #23768971 | 2 |
| #23761847 | 2 |
| #23761732 | 2 |
| #23761266 | 2 |
| #23761265 | 2 |
| C79×#1491 | 2 |
| #9491 | 79 |