Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23782074 | C2 | semidirect |
| 4. #23782059 | C2 | semidirect |
| 5. #23782034 | C2 | semidirect |
| 6. #23782025 | C2 | semidirect |
| 7. #23781923 | C2 | semidirect |
| 9. C4×Dic652 | C2 | semidirect |
| 10. C4×#14579688 | C2 | semidirect |
| 11. C4×M16×C163 | C2 | semidirect |
| 129. C163 | #3172 | semidirect |
| 141. C4×M16 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782222 | 2 |
| #23782199 | 2 |
| #23782074 | 2 |
| #23782059 | 2 |
| #23782034 | 2 |
| #23782025 | 2 |
| #23781923 | 2 |
| #23781911 | 2 |
| C4×Dic652 | 2 |
| C4×#14579688 | 2 |
| C4×M16×C163 | 2 |
| #3172 | 163 |