Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
478 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#19098299 | C2 | semidirect |
| 5. #23761763 | C2 | semidirect |
| 6. #23761288 | C2 | semidirect |
| 7. C79×#1280 | C2 | semidirect |
| 11. #19098894 | C4 | semidirect |
| 12. #19098877 | C4 | semidirect |
| 16. #19098721 | C4 | semidirect |
| 17. #19098704 | C4 | semidirect |
| 240. #1280 | D79 | semidirect |
| 241. C79 | #9263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774183 | 2 |
| #23772454 | 2 |
| #23761902 | 2 |
| C2×#19098299 | 2 |
| #23761763 | 2 |
| #23761288 | 2 |
| C79×#1280 | 2 |
| #9263 | 79 |