Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
536 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 97 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. #23773889 | C2 | semidirect |
| 3. #23765137 | C2 | semidirect |
| 4. #23765120 | C2 | semidirect |
| 5. #23764299 | C2 | semidirect |
| 6. #23761487 | C2 | semidirect |
| 7. C2×#510×C79 | C2 | semidirect |
| 213. C2×#510 | D79 | semidirect |
| 219. C79 | #13335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776534 | 2 |
| #23773889 | 2 |
| #23765137 | 2 |
| #23765120 | 2 |
| #23764299 | 2 |
| #23761487 | 2 |
| C2×#510×C79 | 2 |
| #13335 | 79 |