Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
372 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 57 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. #23768638 | C2 | semidirect |
| 5. #23761426 | C2 | semidirect |
| 6. #23761345 | C2 | semidirect |
| 7. C79×#1353 | C2 | semidirect |
| 177. #1353 | D79 | semidirect |
| 179. C79 | #12181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23768638 | 2 |
| #23764625 | 2 |
| #23762439 | 2 |
| #23762436 | 2 |
| #23761426 | 2 |
| #23761345 | 2 |
| C79×#1353 | 2 |
| #12181 | 79 |