Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
182 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. #23761607 | C2 | semidirect |
| 5. #23761606 | C2 | semidirect |
| 6. #23761605 | C2 | semidirect |
| 7. C79×#1426 | C2 | semidirect |
| 12. #19098396 | C4 | semidirect |
| 13. C32×D79 | C4 | semidirect |
| 93. #1426 | D79 | semidirect |
| 94. C79 | #13638 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M64×D79 | 2 |
| #368×D79 | 2 |
| #23765183 | 2 |
| #23761607 | 2 |
| #23761606 | 2 |
| #23761605 | 2 |
| C79×#1426 | 2 |
| #13638 | 79 |