Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
268 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 268 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 |
|---|---|---|
| 127. C79 | #13509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765189 | 2 |
| #23764149 | 2 |
| #23763563 | 2 |
| #23761509 | 2 |
| #23761508 | 2 |
| #23761481 | 2 |
| C79×#2159 | 2 |
| #13509 | 79 |