Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
144 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 69. C163 | #1684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782017 | 2 |
| #23781957 | 2 |
| #23781951 | 2 |
| #23781789 | 2 |
| #23781417 | 2 |
| #23781412 | 2 |
| #333×C163 | 2 |
| #1684 | 163 |