Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1146 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1146 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 |
|---|---|---|
| 1. C2×#19098940 | C2 | semidirect |
| 2. C2×#19098939 | C2 | semidirect |
| 3. C2×#19098911 | C2 | semidirect |
| 4. #23763064 | C2 | direct (N × H) |
| 5. C2×#19098284 | C2 | semidirect |
| 6. C2×#492×C79 | C2 | semidirect |
| 11. #19098940 | C22 | semidirect |
| 13. #19098939 | C22 | semidirect |
| 15. #19098911 | C22 | semidirect |
| 18. #19098284 | C22 | semidirect |
| 23. #492×C79 | C22 | semidirect |
| 84. C2×C8×C79 | D8 | semidirect |
| 119. C8×C79 | C2×D8 | semidirect |
| 138. C2×C79 | #1721 | semidirect |
| 144. C2×#492 | D79 | semidirect |
| 148. C79 | C2×#1721 | semidirect |
| 160. #492 | C2×D79 | semidirect |
| 226. C2×C8 | #11929609 | semidirect |
| 262. C8 | C2×#11929609 | semidirect |
| 280. C2 | #23763064 | 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×#19098939 | 2 |
| C2×#19098911 | 2 |
| #23763064 | 2 |
| C2×#19098284 | 2 |
| C2×#492×C79 | 2 |
| C2×#1721 | 79 |