Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
372 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 71 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. #23765636 | C2 | semidirect |
| 2. #23765547 | C2 | semidirect |
| 3. #23762913 | C2 | semidirect |
| 4. #23761443 | C2 | semidirect |
| 5. #23761367 | C2 | semidirect |
| 6. #23761358 | C2 | semidirect |
| 8. #19098968 | C22 | semidirect |
| 11. C4⋊(C79⋊C16) | C22 | semidirect |
| 15. #19098339 | C22 | semidirect |
| 16. #19098314 | C22 | semidirect |
| 91. D8×C79 | SD16 | semidirect |
| 174. C79 | #12378 | semidirect |
| 253. D8 | #11929612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765636 | 2 |
| #23765547 | 2 |
| #23762913 | 2 |
| #23761443 | 2 |
| #23761367 | 2 |
| #23761358 | 2 |
| C79×#3273 | 2 |
| #12378 | 79 |