Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
428 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #23772494 | C2 | semidirect |
| 3. #23762131 | C2 | semidirect |
| 6. #23761310 | C2 | semidirect |
| 7. C79×#1287 | C2 | semidirect |
| 175. #1287 | D79 | semidirect |
| 176. C79 | #9530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773500 | 2 |
| #23772494 | 2 |
| #23762131 | 2 |
| #23761826 | 2 |
| #23761740 | 2 |
| #23761310 | 2 |
| C79×#1287 | 2 |
| #9530 | 79 |