Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
628 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 628 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. #23761524 | C2 | semidirect |
| 5. C4×#99×C79 | C2 | semidirect |
| 7. C2×C4×D316 | C4 | semidirect |
| 10. #19098464 | C4 | semidirect |
| 15. #19098428 | C4 | semidirect |
| 17. #19098409 | C4 | semidirect |
| 18. #19098355 | C4 | semidirect |
| 43. #14579076 | C2×C4 | semidirect |
| 61. #99×C79 | C2×C4 | semidirect |
| 67. C2×D316 | C42 | semidirect |
| 93. C4×Dic79 | C42 | semidirect |
| 223. C4×#99 | D79 | semidirect |
| 225. C79 | #12628 | semidirect |
| 276. #99 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766122 | 2 |
| C2×#19098355 | 2 |
| C4×#14579076 | 2 |
| #23761524 | 2 |
| C4×#99×C79 | 2 |
| #12628 | 79 |