Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
888 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 1. #23764229 | C2 | semidirect |
| 2. #23762135 | C2 | semidirect |
| 4. #19098587 | C22 | semidirect |
| 6. C42×Dic79 | C22 | semidirect |
| 9. H(3,𝔽4)×C79 | C4 | semidirect |
| 90. C79 | #8530 | semidirect |
| 91. H(3,𝔽4) | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764229 | 2 |
| #23762135 | 2 |
| C79×#3549 | 2 |
| #8530 | 79 |