Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
162 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 27 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. #23761565 | C2 | semidirect |
| 2. #23761441 | C2 | semidirect |
| 6. #555×C79 | C4 | semidirect |
| 9. #333×C79 | C4 | semidirect |
| 82. C79 | #7519 | semidirect |
| 83. #555 | Dic79 | semidirect |
| 88. #333 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23761565 | 2 |
| #23761441 | 2 |
| C79×#1624 | 2 |
| #7519 | 79 |