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×#19098300 | C2 | semidirect |
| 5. #23761287 | C2 | semidirect |
| 6. #23761242 | C2 | semidirect |
| 7. C79×#1472 | C2 | semidirect |
| 10. #19098893 | C4 | semidirect |
| 11. #19098876 | C4 | semidirect |
| 15. #19098719 | C4 | semidirect |
| 16. #19098702 | C4 | semidirect |
| 238. #1472 | 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 |
|---|---|
| #23774181 | 2 |
| #23772454 | 2 |
| #23761905 | 2 |
| C2×#19098300 | 2 |
| #23761287 | 2 |
| #23761242 | 2 |
| C79×#1472 | 2 |
| #9263 | 79 |