Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
268 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 75 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. #23765627 | C2 | semidirect |
| 4. #23763017 | C2 | semidirect |
| 6. #23761316 | C2 | semidirect |
| 7. C79×#2241 | C2 | semidirect |
| 104. #2241 | D79 | semidirect |
| 110. C79 | #12512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765627 | 2 |
| #23765625 | 2 |
| #23765624 | 2 |
| #23763017 | 2 |
| #23763007 | 2 |
| #23761316 | 2 |
| C79×#2241 | 2 |
| #12512 | 79 |