Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
626 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 127 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. #23772424 | C2 | semidirect |
| 3. #23761824 | C2 | semidirect |
| 4. #23761260 | C2 | semidirect |
| 5. C79×#1800 | C2 | semidirect |
| 37. C4×C79⋊C8 | D4 | semidirect |
| 168. #1800 | D79 | semidirect |
| 171. C79 | #9485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772424 | 2 |
| #23768297 | 2 |
| #23761824 | 2 |
| #23761260 | 2 |
| C79×#1800 | 2 |
| #9485 | 79 |