Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
2022 conjugacy classes of subgroups; only the 587 normal subgroups are shown.
This group has 2022 conjugacy classes of subgroups — too many to draw. Only its 587 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. #23771591 | C2 | direct (N × H) |
| 2. C2×#19098505 | C2 | semidirect |
| 4. C2×#19098482 | C2 | semidirect |
| 11. #19098505 | C22 | semidirect |
| 13. #19098482 | C22 | semidirect |
| 108. C2×C79 | #2835 | semidirect |
| 118. C79 | C2×#2835 | semidirect |
| 219. C2 | #23771591 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771591 | 2 |
| C2×#19098505 | 2 |
| C2×#19098488 | 2 |
| C2×#19098482 | 2 |
| C2×#19098435 | 2 |
| C2×#393×C79 | 2 |
| C2×#2835 | 79 |