Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
982 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 982 conjugacy classes of subgroups — too many to draw. Only its 251 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×#19098911 | C2 | semidirect |
| 3. #23763007 | C2 | direct (N × H) |
| 4. C2×C8×C79⋊C8 | C2 | semidirect |
| 5. C2×#494×C79 | C2 | semidirect |
| 11. #19098911 | C22 | semidirect |
| 14. C8×C79⋊C8 | C22 | semidirect |
| 18. #494×C79 | C22 | semidirect |
| 98. C2×C79 | #1709 | semidirect |
| 102. C2×#494 | D79 | semidirect |
| 107. C79 | C2×#1709 | semidirect |
| 113. #494 | C2×D79 | semidirect |
| 200. C2 | #23763007 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098940 | 2 |
| C2×#19098911 | 2 |
| #23763007 | 2 |
| C2×C8×C79⋊C8 | 2 |
| C2×#494×C79 | 2 |
| C2×#1709 | 79 |