Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
492 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 12. C2×#125×C79 | C4 | semidirect |
| 20. #384×C79 | C4 | semidirect |
| 21. #382×C79 | C4 | semidirect |
| 22. C4×C4⋊C4×C79 | C4 | semidirect |
| 198. C79 | #13300 | semidirect |
| 199. C2×#125 | Dic79 | semidirect |
| 209. #384 | Dic79 | semidirect |
| 210. #382 | Dic79 | semidirect |
| 212. C4×C4⋊C4 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763388 | 2 |
| C4×#14579076 | 2 |
| #23761525 | 2 |
| C79×#2566 | 2 |
| #13300 | 79 |