Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
592 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #23761425 | C2 | semidirect |
| 4. #23761422 | C2 | semidirect |
| 6. C2×#14579140 | C4 | semidirect |
| 8. #19098499 | C4 | semidirect |
| 12. #19098475 | C4 | semidirect |
| 15. #19098423 | C4 | semidirect |
| 23. C22×Dic158 | C2×C4 | semidirect |
| 28. C2×C4⋊Dic79 | C2×C4 | semidirect |
| 44. C79⋊#95 | C2×C4 | semidirect |
| 45. C79⋊#95 | C2×C4 | semidirect |
| 222. C79 | #11716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769205 | 2 |
| C2×#19098330 | 2 |
| #23761425 | 2 |
| #23761422 | 2 |
| C2×#323×C79 | 2 |
| #11716 | 79 |