Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
424 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 4. #23761421 | C2 | semidirect |
| 5. #23761400 | C2 | semidirect |
| 6. #23761348 | C2 | semidirect |
| 7. C79×#2523 | C2 | semidirect |
| 196. #2523 | D79 | semidirect |
| 203. C79 | #12134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764651 | 2 |
| #23762385 | 2 |
| #23762351 | 2 |
| #23761421 | 2 |
| #23761400 | 2 |
| #23761348 | 2 |
| C79×#2523 | 2 |
| #12134 | 79 |