Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
622 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 113 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. #23766017 | C2 | semidirect |
| 4. C2×#19098288 | C2 | semidirect |
| 5. #23761268 | C2 | semidirect |
| 6. #23761267 | C2 | semidirect |
| 12. #19098494 | C4 | semidirect |
| 14. #19098477 | C4 | semidirect |
| 236. C79 | #9204 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769144 | 2 |
| #23766017 | 2 |
| #23761968 | 2 |
| C2×#19098288 | 2 |
| #23761268 | 2 |
| #23761267 | 2 |
| C79×#1519 | 2 |
| #9204 | 79 |