Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
400 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 141 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. #23782222 | C2 | semidirect |
| 3. #23782020 | C2 | semidirect |
| 4. #23782016 | C2 | semidirect |
| 5. #23782012 | C2 | semidirect |
| 6. #23781662 | C2 | semidirect |
| 7. C2×C4×C8×C163 | C2 | semidirect |
| 78. C163 | #3131 | semidirect |
| 86. C2×C4×C8 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782222 | 2 |
| #23782215 | 2 |
| #23782020 | 2 |
| #23782016 | 2 |
| #23782012 | 2 |
| #23781662 | 2 |
| C2×C4×C8×C163 | 2 |
| #3131 | 163 |