Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
560 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 2. #23763499 | C2 | semidirect |
| 4. #23761286 | C2 | semidirect |
| 16. #400×C79 | C4 | semidirect |
| 17. #399×C79 | C4 | semidirect |
| 18. #398×C79 | C4 | semidirect |
| 20. #397×C79 | C4 | semidirect |
| 189. C79 | #9011 | semidirect |
| 197. #400 | Dic79 | semidirect |
| 198. #399 | Dic79 | semidirect |
| 199. #398 | Dic79 | semidirect |
| 201. #397 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772429 | 2 |
| #23763499 | 2 |
| C4×#14579076 | 2 |
| #23761286 | 2 |
| C79×#2395 | 2 |
| #9011 | 79 |