Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
522 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #23761233 | C2 | semidirect |
| 4. #23761228 | C2 | semidirect |
| 5. C79×#1276 | C2 | semidirect |
| 25. #14579118 | C8 | semidirect |
| 153. #1276 | D79 | semidirect |
| 155. C79 | #8731 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579118 | 2 |
| #23761712 | 2 |
| #23761233 | 2 |
| #23761228 | 2 |
| C79×#1276 | 2 |
| #8731 | 79 |