Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
452 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #23761407 | C2 | semidirect |
| 5. #23761406 | C2 | semidirect |
| 6. #23761405 | C2 | semidirect |
| 7. C79×#1346 | C2 | semidirect |
| 193. #1346 | D79 | semidirect |
| 194. C79 | #11700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769168 | 2 |
| #23763137 | 2 |
| #23761713 | 2 |
| #23761407 | 2 |
| #23761406 | 2 |
| #23761405 | 2 |
| C79×#1346 | 2 |
| #11700 | 79 |