Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
406 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 111 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. #23765199 | C2 | semidirect |
| 2. #23762163 | C2 | semidirect |
| 3. #23761443 | C2 | semidirect |
| 6. C4⋊(C79⋊C16) | C22 | semidirect |
| 10. #19098314 | C22 | semidirect |
| 137. C79 | #11957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765199 | 2 |
| #23762163 | 2 |
| #23761443 | 2 |
| C2×#495×C79 | 2 |
| #11957 | 79 |