Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
534 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23763543 | C2 | semidirect |
| 2. #23763149 | C2 | semidirect |
| 3. #23761221 | C2 | semidirect |
| 157. C79 | #7699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763543 | 2 |
| #23763149 | 2 |
| #23761221 | 2 |
| C79×#2858 | 2 |
| #7699 | 79 |