Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
378 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 378 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 |
|---|---|---|
| 2. #23765159 | C2 | semidirect |
| 5. #23761513 | C2 | semidirect |
| 6. #23761495 | C2 | semidirect |
| 7. C79×#1833 | C2 | semidirect |
| 12. #19098686 | C4 | semidirect |
| 145. #1833 | D79 | semidirect |
| 148. C79 | #12830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772318 | 2 |
| #23765159 | 2 |
| #23765135 | 2 |
| C2×#19098369 | 2 |
| #23761513 | 2 |
| #23761495 | 2 |
| C79×#1833 | 2 |
| #12830 | 79 |