Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
582 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 1. C22×C4×Dic163 | C2 | semidirect |
| 2. #23781553 | C2 | semidirect |
| 3. #23781546 | C2 | semidirect |
| 5. #23781537 | C2 | semidirect |
| 6. #23781528 | C2 | semidirect |
| 84. C163 | #2853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic163 | 2 |
| #23781553 | 2 |
| #23781546 | 2 |
| #23781545 | 2 |
| #23781537 | 2 |
| #23781528 | 2 |
| C2×#123×C163 | 2 |
| #2853 | 163 |