Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
542 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23774712 | C2 | semidirect |
| 2. #23773495 | C2 | semidirect |
| 4. #23764198 | C2 | semidirect |
| 5. #23762010 | C2 | semidirect |
| 6. #23761269 | C2 | semidirect |
| 7. C79×#1531 | C2 | semidirect |
| 211. #1531 | D79 | semidirect |
| 214. C79 | #10027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774712 | 2 |
| #23773495 | 2 |
| #23773492 | 2 |
| #23764198 | 2 |
| #23762010 | 2 |
| #23761269 | 2 |
| C79×#1531 | 2 |
| #10027 | 79 |