Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
182 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 63 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. #23765272 | C2 | semidirect |
| 3. #23761607 | C2 | semidirect |
| 4. #23761592 | C2 | semidirect |
| 6. #23761536 | C2 | semidirect |
| 10. #19098403 | C4 | semidirect |
| 11. #19098401 | C4 | semidirect |
| 91. C79 | #13657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765717 | 2 |
| #23765272 | 2 |
| #23761607 | 2 |
| #23761592 | 2 |
| #23761587 | 2 |
| #23761536 | 2 |
| C79×#2179 | 2 |
| #13657 | 79 |