Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
612 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 119 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. #23761972 | C2 | semidirect |
| 4. #23761267 | C2 | semidirect |
| 15. #399×C79 | C4 | semidirect |
| 17. #393×C79 | C4 | semidirect |
| 176. C79 | #9201 | semidirect |
| 180. #399 | Dic79 | semidirect |
| 182. #393 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765998 | 2 |
| #23761972 | 2 |
| C2×#19098287 | 2 |
| #23761267 | 2 |
| C79×#2626 | 2 |
| #9201 | 79 |