Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
484 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 83 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×#19098362 | C2 | semidirect |
| 2. C2×#19098312 | C2 | semidirect |
| 3. #23761554 | C2 | direct (N × H) |
| 8. #19098362 | C22 | semidirect |
| 10. #19098312 | C22 | semidirect |
| 169. C2×C79 | #1405 | semidirect |
| 175. C79 | C2×#1405 | semidirect |
| 339. C2 | #23761554 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098362 | 2 |
| C2×#19098312 | 2 |
| #23761554 | 2 |
| C2×#456×C79 | 2 |
| C2×#1405 | 79 |