Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
466 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23762148 | C2 | semidirect |
| 4. #23761295 | C2 | semidirect |
| 5. C79×#1837 | C2 | semidirect |
| 138. #1837 | D79 | semidirect |
| 142. C79 | #8660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×D316 | 2 |
| #23762148 | 2 |
| #23761824 | 2 |
| #23761295 | 2 |
| C79×#1837 | 2 |
| #8660 | 79 |