Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
184 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 67 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. #23765282 | C2 | semidirect |
| 3. #23761604 | C2 | semidirect |
| 4. #23761585 | C2 | semidirect |
| 5. C79×#1397 | C2 | semidirect |
| 8. Dic1264 | C4 | semidirect |
| 9. #19098402 | C4 | semidirect |
| 10. D2528 | C4 | semidirect |
| 66. #1397 | D79 | semidirect |
| 67. C79 | #13656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765709 | 2 |
| #23765282 | 2 |
| #23761604 | 2 |
| #23761585 | 2 |
| C79×#1397 | 2 |
| #13656 | 79 |