Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
544 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 81 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. #23774399 | C2 | semidirect |
| 3. #23761869 | C2 | semidirect |
| 4. #23761821 | C2 | semidirect |
| 5. #23761753 | C2 | semidirect |
| 6. #23761273 | C2 | semidirect |
| 7. C79×#3235 | C2 | semidirect |
| 202. #3235 | D79 | semidirect |
| 209. C79 | #10121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774399 | 2 |
| #23773868 | 2 |
| #23761869 | 2 |
| #23761821 | 2 |
| #23761753 | 2 |
| #23761273 | 2 |
| C79×#3235 | 2 |
| #10121 | 79 |