Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
372 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 93 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. #23763574 | C2 | semidirect |
| 3. #23762170 | C2 | semidirect |
| 6. #23761230 | C2 | semidirect |
| 7. C79×#1570 | C2 | semidirect |
| 138. #1570 | D79 | semidirect |
| 142. C79 | #10661 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764197 | 2 |
| #23763574 | 2 |
| #23762170 | 2 |
| #23761826 | 2 |
| #23761824 | 2 |
| #23761230 | 2 |
| C79×#1570 | 2 |
| #10661 | 79 |