Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
304 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 41 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. #23761527 | C2 | semidirect |
| 3. C79×#1319 | C2 | semidirect |
| 115. #1319 | D79 | semidirect |
| 116. C79 | #7404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764487 | 2 |
| #23761527 | 2 |
| C79×#1319 | 2 |
| #7404 | 79 |