Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
500 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23763396 | C2 | semidirect |
| 4. #23761526 | C2 | semidirect |
| 5. C79×#1801 | C2 | semidirect |
| 188. C4×C79 | #355 | semidirect |
| 202. #1801 | D79 | semidirect |
| 204. C79 | #12801 | semidirect |
| 390. C4 | #19098359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579150 | 2 |
| C2×#19098359 | 2 |
| #23763396 | 2 |
| #23761526 | 2 |
| C79×#1801 | 2 |
| #12801 | 79 |