Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
388 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23762163 | C2 | semidirect |
| 4. #23761310 | C2 | semidirect |
| 5. C79×#1568 | C2 | semidirect |
| 132. #1568 | D79 | semidirect |
| 135. C79 | #8630 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772113 | 2 |
| #23762163 | 2 |
| #23762034 | 2 |
| #23761310 | 2 |
| C79×#1568 | 2 |
| #8630 | 79 |