Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1168 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 115 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×#19098351 | C2 | semidirect |
| 3. #23763318 | C2 | semidirect |
| 4. C79×#1785 | C2 | semidirect |
| 5. C23×D316 | C4 | semidirect |
| 11. C2×#14579129 | C4 | semidirect |
| 13. C2×#14579120 | C4 | semidirect |
| 213. #1785 | D79 | semidirect |
| 215. C79 | #12691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099127 | 2 |
| C2×#19098351 | 2 |
| #23763318 | 2 |
| C79×#1785 | 2 |
| #12691 | 79 |