Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
3754 conjugacy classes of subgroups; only the 555 normal subgroups are shown.
This group has 3754 conjugacy classes of subgroups — too many to draw. Only its 555 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×#19098537 | C2 | semidirect |
| 2. #23765992 | C2 | semidirect |
| 3. #23763348 | C2 | semidirect |
| 5. C2×#14579120 | C22 | semidirect |
| 6. C22×C4⋊Dic79 | C22 | semidirect |
| 8. C2×#14579076 | C22 | semidirect |
| 11. #19098443 | C22 | semidirect |
| 14. #585×C79 | C4 | semidirect |
| 79. C2×Q8×C79 | C22⋊C4 | semidirect |
| 88. C2×D4×C79 | C22⋊C4 | semidirect |
| 96. C22×C4×C79 | C22⋊C4 | semidirect |
| 167. C79 | #20610 | semidirect |
| 169. #585 | Dic79 | semidirect |
| 233. C2×Q8 | C22⋊Dic79 | semidirect |
| 242. C2×D4 | C22⋊Dic79 | semidirect |
| 253. C22×C4 | C22⋊Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098537 | 2 |
| #23765992 | 2 |
| #23763348 | 2 |
| C2×#585×C79 | 2 |
| #20610 | 79 |