Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
724 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 724 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. C2×#19098353 | C2 | semidirect |
| 4. #23761518 | C2 | semidirect |
| 15. C2×#123×C79 | C4 | semidirect |
| 17. C22×C4⋊C4×C79 | C4 | semidirect |
| 20. #386×C79 | C4 | semidirect |
| 24. #381×C79 | C4 | semidirect |
| 249. C79 | #13085 | semidirect |
| 251. C2×#123 | Dic79 | semidirect |
| 254. C22×C4⋊C4 | Dic79 | semidirect |
| 263. #386 | Dic79 | semidirect |
| 267. #381 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098537 | 2 |
| C2×#19098353 | 2 |
| #23763328 | 2 |
| #23761518 | 2 |
| C79×#2406 | 2 |
| #13085 | 79 |