Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
882 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 882 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 1. C2×C79⋊#564 | C2 | semidirect |
| 4. #23762703 | C2 | direct (N × H) |
| 5. C2×#19098304 | C2 | semidirect |
| 6. C2×#330×C79 | C2 | semidirect |
| 9. C79⋊#564 | C22 | semidirect |
| 23. #19098304 | C22 | semidirect |
| 26. #330×C79 | C22 | semidirect |
| 136. C2×C79 | #1658 | semidirect |
| 145. C2×#330 | D79 | semidirect |
| 146. C79 | C2×#1658 | semidirect |
| 166. #330 | C2×D79 | semidirect |
| 276. C2 | #23762703 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C79⋊#564 | 2 |
| C2×#19098929 | 2 |
| C2×#19098928 | 2 |
| #23762703 | 2 |
| C2×#19098304 | 2 |
| C2×#330×C79 | 2 |
| C2×#1658 | 79 |