Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
518 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 79 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. #23773953 | C2 | semidirect |
| 4. #23762026 | C2 | semidirect |
| 6. #23761264 | C2 | semidirect |
| 7. C79×#1515 | C2 | semidirect |
| 199. #1515 | D79 | semidirect |
| 202. C79 | #10023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773953 | 2 |
| #23773495 | 2 |
| #23769271 | 2 |
| #23762026 | 2 |
| #23761842 | 2 |
| #23761264 | 2 |
| C79×#1515 | 2 |
| #10023 | 79 |