Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
2286 conjugacy classes of subgroups; only the 555 normal subgroups are shown.
This group has 2286 conjugacy classes of subgroups — too many to draw. Only its 555 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 |
|---|---|---|
| 1. C2×#19098431 | C2 | semidirect |
| 2. #23761627 | C2 | semidirect |
| 11. C22×C42×C79 | C4 | semidirect |
| 52. C42×C79 | C22⋊C4 | semidirect |
| 78. C22×C79 | #383 | semidirect |
| 98. C79 | #14683 | semidirect |
| 102. C22×C42 | Dic79 | semidirect |
| 146. C42 | C22⋊Dic79 | semidirect |
| 172. C22 | #19098431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098431 | 2 |
| #23761627 | 2 |
| #23761623 | 2 |
| C23×C42×C79 | 2 |
| #14683 | 79 |