Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
350 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 10. #19098690 | C4 | semidirect |
| 12. #19098687 | C4 | semidirect |
| 157. C79 | #8679 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772330 | 2 |
| #23763530 | 2 |
| #23762146 | 2 |
| #23761965 | 2 |
| #23761963 | 2 |
| #23761260 | 2 |
| C79×#1286 | 2 |
| #8679 | 79 |