Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
314 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23765172 | C2 | semidirect |
| 4. #23763286 | C2 | semidirect |
| 5. #23761504 | C2 | semidirect |
| 6. #23761483 | C2 | semidirect |
| 16. #19098379 | C4 | semidirect |
| 17. #19098376 | C4 | semidirect |
| 146. C79 | #13140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765172 | 2 |
| #23765149 | 2 |
| #23764294 | 2 |
| #23763286 | 2 |
| #23761504 | 2 |
| #23761483 | 2 |
| C79×#2145 | 2 |
| #13140 | 79 |