Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
270 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 270 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 |
|---|---|---|
| 16. #19098285 | C4 | semidirect |
| 17. #19098284 | C4 | semidirect |
| 132. C79 | #8794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763571 | 2 |
| #23763530 | 2 |
| #23761693 | 2 |
| #23761260 | 2 |
| #23761259 | 2 |
| #23761258 | 2 |
| C79×#1286 | 2 |
| #8794 | 79 |