Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
552 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 5. C2×#14579161 | C4 | semidirect |
| 10. #19098468 | C4 | semidirect |
| 13. C4×C4⋊Dic79 | C4 | semidirect |
| 162. C4×C79 | #354 | semidirect |
| 179. C79 | #13224 | semidirect |
| 340. C4 | #19098357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23768392 | 2 |
| C2×#19098357 | 2 |
| C4×#14579076 | 2 |
| C79×#1799 | 2 |
| #13224 | 79 |