Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
528 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 119 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. C2×C22⋊(C79⋊C16) | C2 | semidirect |
| 3. #23761325 | C2 | semidirect |
| 4. C79×#2112 | C2 | semidirect |
| 15. C22⋊(C79⋊C16) | C22 | semidirect |
| 19. C22⋊C16×C79 | C22 | semidirect |
| 165. #2112 | D79 | semidirect |
| 168. C79 | #11422 | semidirect |
| 183. C22⋊C16 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098529 | 2 |
| C2×C22⋊(C79⋊C16) | 2 |
| #23761325 | 2 |
| C79×#2112 | 2 |
| #11422 | 79 |