Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
430 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23765155 | C2 | semidirect |
| 5. #23763561 | C2 | semidirect |
| 6. #23761505 | C2 | semidirect |
| 7. C79×#1386 | C2 | semidirect |
| 11. #19098657 | C4 | semidirect |
| 13. #19098645 | C4 | semidirect |
| 164. #1386 | D79 | semidirect |
| 165. C79 | #12817 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772171 | 2 |
| #23765155 | 2 |
| C2×#19098374 | 2 |
| C2×#19098372 | 2 |
| #23763561 | 2 |
| #23761505 | 2 |
| C79×#1386 | 2 |
| #12817 | 79 |