Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
488 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 97 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. #23774546 | C2 | semidirect |
| 4. #23764220 | C2 | semidirect |
| 5. #23761965 | C2 | semidirect |
| 7. C79×#1281 | C2 | semidirect |
| 188. #1281 | D79 | semidirect |
| 189. C79 | #10226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774546 | 2 |
| #23774523 | 2 |
| #23773746 | 2 |
| #23764220 | 2 |
| #23761965 | 2 |
| #23761961 | 2 |
| C79×#1281 | 2 |
| #10226 | 79 |