Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
492 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 143 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. #23763517 | C2 | semidirect |
| 2. #23761226 | C2 | semidirect |
| 23. #124×C79 | C8 | semidirect |
| 142. C79 | #7601 | semidirect |
| 160. #124 | C79⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763517 | 2 |
| #23761226 | 2 |
| #23761221 | 2 |
| C4×#124×C79 | 2 |
| #7601 | 79 |