Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
478 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 93 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. #23772054 | C2 | semidirect |
| 3. #23763497 | C2 | semidirect |
| 5. #23761276 | C2 | semidirect |
| 6. #23761246 | C2 | semidirect |
| 16. C2×#14579094 | C4 | semidirect |
| 17. C2×#14579092 | C4 | semidirect |
| 19. C2×#14579082 | C4 | semidirect |
| 20. C2×#14579082 | C4 | 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×#19098884 | 2 |
| #23772054 | 2 |
| #23763497 | 2 |
| #23761916 | 2 |
| #23761276 | 2 |
| #23761246 | 2 |
| C79×#1471 | 2 |
| #9242 | 79 |