Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
478 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23772058 | C2 | semidirect |
| 5. #23761276 | C2 | semidirect |
| 6. #23761248 | C2 | semidirect |
| 7. C79×#1826 | C2 | semidirect |
| 16. C2×#14579094 | C4 | semidirect |
| 17. C2×#14579092 | C4 | semidirect |
| 19. C2×#14579081 | C4 | semidirect |
| 20. C2×#14579081 | C4 | semidirect |
| 226. #1826 | D79 | semidirect |
| 231. C79 | #9242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098887 | 2 |
| #23772058 | 2 |
| #23761915 | 2 |
| #23761761 | 2 |
| #23761276 | 2 |
| #23761248 | 2 |
| C79×#1826 | 2 |
| #9242 | 79 |