Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
540 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 540 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 |
|---|---|---|
| 7. C22×C4×Dic79 | C4 | semidirect |
| 12. #19098435 | C4 | semidirect |
| 13. #19098424 | C4 | semidirect |
| 17. C4×C22⋊Dic79 | C4 | semidirect |
| 75. C22×Dic79 | C4⋊C4 | semidirect |
| 87. C22⋊Dic79 | C4⋊C4 | semidirect |
| 198. C4×C79 | #352 | semidirect |
| 219. C79 | #12794 | semidirect |
| 417. C4 | #19098354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579142 | 2 |
| C2×#19098354 | 2 |
| #23763388 | 2 |
| #23761519 | 2 |
| C79×#1800 | 2 |
| #12794 | 79 |