Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
464 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23765011 | C2 | semidirect |
| 3. #23761408 | C2 | semidirect |
| 4. C79×#1807 | C2 | semidirect |
| 5. C22×D632 | C4 | semidirect |
| 10. #19098799 | C4 | semidirect |
| 12. C2×#14579095 | C4 | semidirect |
| 15. C22⋊(C79⋊C16) | C22 | semidirect |
| 19. #340×C79 | C22 | semidirect |
| 157. #1807 | D79 | semidirect |
| 159. C79 | #11888 | semidirect |
| 174. #340 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098799 | 2 |
| #23765011 | 2 |
| #23761408 | 2 |
| C79×#1807 | 2 |
| #11888 | 79 |