Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
408 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. #23762086 | C2 | semidirect |
| 4. #23762080 | C2 | semidirect |
| 6. #23761297 | C2 | semidirect |
| 7. C79×#1571 | C2 | semidirect |
| 164. #1571 | D79 | semidirect |
| 169. C79 | #10453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098854 | 2 |
| #23763389 | 2 |
| #23762086 | 2 |
| #23762080 | 2 |
| #23761790 | 2 |
| #23761297 | 2 |
| C79×#1571 | 2 |
| #10453 | 79 |