Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
| 2. #23782075 | C2 | semidirect |
| 3. #23782060 | C2 | semidirect |
| 4. #23782035 | C2 | semidirect |
| 5. #23782024 | C2 | semidirect |
| 6. #23781921 | C2 | semidirect |
| 8. C4×#14579689 | C2 | semidirect |
| 9. C4×#14579687 | C2 | semidirect |
| 10. C4×#14579683 | C2 | semidirect |
| 129. C163 | #3172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782222 | 2 |
| #23782075 | 2 |
| #23782060 | 2 |
| #23782035 | 2 |
| #23782024 | 2 |
| #23781921 | 2 |
| #23781909 | 2 |
| C4×#14579689 | 2 |
| C4×#14579687 | 2 |
| C4×#14579683 | 2 |
| #529×C163 | 2 |
| #3172 | 163 |