Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
316 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 53 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. #23782291 | C2 | semidirect |
| 2. #23781816 | C2 | semidirect |
| 3. #23781401 | C2 | semidirect |
| 4. #23781389 | C2 | semidirect |
| 20. C2×Dic326 | D4 | semidirect |
| 26. C4⋊Dic163 | D4 | semidirect |
| 61. C23×C163 | SD16 | semidirect |
| 102. C163 | #1596 | semidirect |
| 157. C23 | #14579687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782291 | 2 |
| #23781816 | 2 |
| #23781401 | 2 |
| #23781389 | 2 |
| #392×C163 | 2 |
| #1596 | 163 |