Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
418 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 418 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. #23765156 | C2 | semidirect |
| 3. #23761442 | C2 | semidirect |
| 4. C79×#1564 | C2 | semidirect |
| 15. C4⋊(C79⋊C16) | C22 | semidirect |
| 19. #334×C79 | C22 | semidirect |
| 140. #1564 | D79 | semidirect |
| 142. C79 | #11926 | semidirect |
| 157. #334 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098947 | 2 |
| #23765156 | 2 |
| #23761442 | 2 |
| C79×#1564 | 2 |
| #11926 | 79 |