Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
418 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 418 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. #23763530 | C2 | semidirect |
| 3. #23762146 | C2 | semidirect |
| 6. #23761260 | C2 | semidirect |
| 7. C79×#1286 | C2 | semidirect |
| 11. #19098640 | C4 | semidirect |
| 13. #19098628 | C4 | semidirect |
| 175. #1286 | D79 | semidirect |
| 176. C79 | #8680 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772111 | 2 |
| #23763530 | 2 |
| #23762146 | 2 |
| #23761961 | 2 |
| #23761959 | 2 |
| #23761260 | 2 |
| C79×#1286 | 2 |
| #8680 | 79 |