Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
494 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 3. #23763557 | C2 | semidirect |
| 4. #23763528 | C2 | semidirect |
| 5. C79×#1273 | C2 | semidirect |
| 113. #1273 | D79 | semidirect |
| 114. C79 | #10677 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764206 | 2 |
| #23763557 | 2 |
| #23763528 | 2 |
| C79×#1273 | 2 |
| #10677 | 79 |