Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
608 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 127 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. #23763543 | C2 | semidirect |
| 3. #23761220 | C2 | semidirect |
| 4. C79×#1839 | C2 | semidirect |
| 26. #14579158 | C8 | semidirect |
| 160. #1839 | D79 | semidirect |
| 162. C79 | #7603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579158 | 2 |
| #23763543 | 2 |
| #23761220 | 2 |
| C79×#1839 | 2 |
| #7603 | 79 |