Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
216 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 112. C79 | #13545 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764178 | 2 |
| #23763525 | 2 |
| #23761515 | 2 |
| #23761511 | 2 |
| #23761507 | 2 |
| #23761487 | 2 |
| C79×#1383 | 2 |
| #13545 | 79 |