Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
412 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23761846 | C2 | semidirect |
| 5. #23761743 | C2 | semidirect |
| 6. #23761273 | C2 | semidirect |
| 7. C79×#1308 | C2 | semidirect |
| 200. #1308 | D79 | semidirect |
| 202. C79 | #9531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773573 | 2 |
| #23772380 | 2 |
| #23762032 | 2 |
| #23761846 | 2 |
| #23761743 | 2 |
| #23761273 | 2 |
| C79×#1308 | 2 |
| #9531 | 79 |