Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
742 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 742 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23774157 | C2 | semidirect |
| 2. #23772660 | C2 | semidirect |
| 3. #23763312 | C2 | semidirect |
| 4. #23761765 | C2 | semidirect |
| 5. #23761760 | C2 | semidirect |
| 6. #23761276 | C2 | semidirect |
| 254. C79 | #9975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774157 | 2 |
| #23772660 | 2 |
| #23763312 | 2 |
| #23761765 | 2 |
| #23761760 | 2 |
| #23761276 | 2 |
| C79×#3006 | 2 |
| #9975 | 79 |