Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
636 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 123 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. C4×#14579076 | C2 | semidirect |
| 4. #23761519 | C2 | semidirect |
| 5. C4×#100×C79 | C2 | semidirect |
| 7. C22×(C2×D79)⋊C4 | C4 | semidirect |
| 14. #19098435 | C4 | semidirect |
| 15. #19098418 | C4 | semidirect |
| 17. C4×C22⋊Dic79 | C4 | semidirect |
| 18. #19098351 | C4 | semidirect |
| 69. C23×D79 | C42 | semidirect |
| 85. C22⋊Dic79 | C42 | semidirect |
| 226. C4×#100 | D79 | semidirect |
| 229. C79 | #12622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766054 | 2 |
| C2×#19098351 | 2 |
| C4×#14579076 | 2 |
| #23761519 | 2 |
| C4×#100×C79 | 2 |
| #12622 | 79 |