Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
520 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23776536 | C2 | semidirect |
| 2. #23773120 | C2 | semidirect |
| 3. C2×#19098371 | C2 | semidirect |
| 4. #23761504 | C2 | semidirect |
| 5. C79×#2113 | C2 | semidirect |
| 140. #2113 | D79 | semidirect |
| 142. C79 | #13312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776536 | 2 |
| #23773120 | 2 |
| C2×#19098371 | 2 |
| #23761504 | 2 |
| C79×#2113 | 2 |
| #13312 | 79 |