Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
446 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. #23761421 | C2 | semidirect |
| 4. #23761400 | C2 | semidirect |
| 12. C2×C4×Q8×C79 | C4 | semidirect |
| 15. #397×C79 | C4 | semidirect |
| 18. #393×C79 | C4 | semidirect |
| 22. #376×C79 | C4 | semidirect |
| 191. C79 | #11823 | semidirect |
| 192. C2×C4×Q8 | Dic79 | semidirect |
| 197. #397 | Dic79 | semidirect |
| 200. #393 | Dic79 | semidirect |
| 205. #376 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763388 | 2 |
| #23761738 | 2 |
| #23761421 | 2 |
| #23761400 | 2 |
| C79×#2398 | 2 |
| #11823 | 79 |