Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
360 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23765189 | C2 | semidirect |
| 4. #23763281 | C2 | semidirect |
| 5. #23761509 | C2 | semidirect |
| 6. #23761481 | C2 | semidirect |
| 17. #19098376 | C4 | semidirect |
| 157. C79 | #13136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765189 | 2 |
| C2×#19098376 | 2 |
| #23764267 | 2 |
| #23763281 | 2 |
| #23761509 | 2 |
| #23761481 | 2 |
| C79×#2140 | 2 |
| #13136 | 79 |