Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
284 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 63 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. #23765717 | C2 | semidirect |
| 2. #23765508 | C2 | semidirect |
| 3. #23761587 | C2 | semidirect |
| 4. #23761540 | C2 | semidirect |
| 6. C2×Dic632 | C22 | semidirect |
| 10. #19098397 | C22 | semidirect |
| 11. #19098391 | C22 | semidirect |
| 113. C79 | #13668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765717 | 2 |
| #23765508 | 2 |
| #23761587 | 2 |
| #23761540 | 2 |
| C79×#3414 | 2 |
| #13668 | 79 |