Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1030 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 1030 conjugacy classes of subgroups — too many to draw. Only its 267 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×#19098961 | C2 | semidirect |
| 3. C2×#19098936 | C2 | semidirect |
| 4. C2×#19098910 | C2 | semidirect |
| 5. #23763028 | C2 | direct (N × H) |
| 6. C2×#322×C79 | C2 | semidirect |
| 13. #19098961 | C22 | semidirect |
| 17. #19098936 | C22 | semidirect |
| 19. #19098910 | C22 | semidirect |
| 24. #322×C79 | C22 | semidirect |
| 82. C2×C8×C79 | SD16 | semidirect |
| 114. C8×C79 | C2×SD16 | semidirect |
| 130. C2×C79 | #1715 | semidirect |
| 140. C2×#322 | D79 | semidirect |
| 141. C79 | C2×#1715 | semidirect |
| 159. #322 | C2×D79 | semidirect |
| 213. C2×C8 | #11929613 | semidirect |
| 249. C8 | C2×#11929613 | semidirect |
| 266. C2 | #23763028 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098961 | 2 |
| C2×#19098940 | 2 |
| C2×#19098936 | 2 |
| C2×#19098910 | 2 |
| #23763028 | 2 |
| C2×#322×C79 | 2 |
| C2×#1715 | 79 |