Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
408 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 14. #125×C163 | C4 | semidirect |
| 61. C163 | #2382 | semidirect |
| 68. #125 | Dic163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781564 | 2 |
| #23781551 | 2 |
| #23781531 | 2 |
| C2×#125×C163 | 2 |
| #2382 | 163 |