Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
418 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 79 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. #23765623 | C2 | semidirect |
| 2. #23765547 | C2 | semidirect |
| 3. #23762799 | C2 | semidirect |
| 4. #23761446 | C2 | semidirect |
| 5. #23761361 | C2 | semidirect |
| 6. D4⋊(C79⋊C16) | C2 | semidirect |
| 8. #19098968 | C22 | semidirect |
| 11. C4⋊(C79⋊C16) | C22 | semidirect |
| 14. C4×C79⋊C16 | C22 | semidirect |
| 15. #19098316 | C22 | semidirect |
| 157. C79 | #12372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765623 | 2 |
| #23765547 | 2 |
| #23762799 | 2 |
| #23761446 | 2 |
| #23761361 | 2 |
| D4⋊(C79⋊C16) | 2 |
| D4×D8×C79 | 2 |
| #12372 | 79 |