Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
226 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 69 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. #23761464 | C2 | semidirect |
| 4. #23761458 | C2 | semidirect |
| 5. C79×#1713 | C2 | semidirect |
| 86. #1713 | D79 | semidirect |
| 90. C79 | #12499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765544 | 2 |
| #23762286 | 2 |
| #23761464 | 2 |
| #23761458 | 2 |
| C79×#1713 | 2 |
| #12499 | 79 |