Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
508 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. #23766117 | C2 | semidirect |
| 4. #23762073 | C2 | semidirect |
| 6. #23761228 | C2 | semidirect |
| 7. C79×#1286 | C2 | semidirect |
| 11. #19098968 | C4 | semidirect |
| 12. #19098910 | C4 | semidirect |
| 193. #1286 | D79 | semidirect |
| 195. C79 | #9300 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774523 | 2 |
| #23766117 | 2 |
| #23764231 | 2 |
| #23762073 | 2 |
| #23761959 | 2 |
| #23761228 | 2 |
| C79×#1286 | 2 |
| #9300 | 79 |