Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
180 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 51 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. C2×#19098403 | C2 | semidirect |
| 5. #23761603 | C2 | semidirect |
| 6. #23761594 | C2 | semidirect |
| 7. C79×#1420 | C2 | semidirect |
| 96. #1420 | D79 | semidirect |
| 97. C79 | #13701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098403 | 2 |
| #23765695 | 2 |
| #23765526 | 2 |
| #23765522 | 2 |
| #23761603 | 2 |
| #23761594 | 2 |
| C79×#1420 | 2 |
| #13701 | 79 |