Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
496 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23769519 | C2 | semidirect |
| 4. #23762116 | C2 | semidirect |
| 5. #23762001 | C2 | semidirect |
| 7. C79×#1300 | C2 | semidirect |
| 180. #1300 | D79 | semidirect |
| 181. C79 | #10093 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774592 | 2 |
| #23773794 | 2 |
| #23769519 | 2 |
| #23762116 | 2 |
| #23762001 | 2 |
| #23761907 | 2 |
| C79×#1300 | 2 |
| #10093 | 79 |