Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
302 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 115 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×#19098397 | C2 | semidirect |
| 2. C2×#19098389 | C2 | semidirect |
| 3. #23761581 | C2 | semidirect |
| 4. #23761578 | C2 | semidirect |
| 13. #508×C79 | C4 | semidirect |
| 30. Q32×C79 | C2×C4 | semidirect |
| 33. D16×C79 | C2×C4 | semidirect |
| 101. C79 | #13616 | semidirect |
| 104. #508 | Dic79 | semidirect |
| 123. Q32 | C2×Dic79 | semidirect |
| 126. D16 | C2×Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098397 | 2 |
| C2×#19098389 | 2 |
| #23761581 | 2 |
| #23761578 | 2 |
| C2×#508×C79 | 2 |
| #13616 | 79 |