Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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. #23776502 | C2 | semidirect |
| 3. C2×#19098374 | C2 | semidirect |
| 4. #23765127 | C2 | semidirect |
| 5. #23763456 | C2 | semidirect |
| 6. #23761500 | C2 | semidirect |
| 7. C79×#1388 | C2 | semidirect |
| 15. #19098839 | C4 | semidirect |
| 16. #19098834 | C4 | semidirect |
| 184. #1388 | D79 | semidirect |
| 186. C79 | #13070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776502 | 2 |
| #23773121 | 2 |
| C2×#19098374 | 2 |
| #23765127 | 2 |
| #23763456 | 2 |
| #23761500 | 2 |
| C79×#1388 | 2 |
| #13070 | 79 |