Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
176 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 176 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. #23782012 | C2 | semidirect |
| 2. #23781956 | C2 | semidirect |
| 4. C8×D652 | C2 | semidirect |
| 5. #23781413 | C2 | semidirect |
| 6. #23781408 | C2 | semidirect |
| 7. #334×C163 | C2 | semidirect |
| 82. C163 | #1677 | semidirect |
| 88. #334 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782012 | 2 |
| #23781956 | 2 |
| #23781861 | 2 |
| C8×D652 | 2 |
| #23781413 | 2 |
| #23781408 | 2 |
| #334×C163 | 2 |
| #1677 | 163 |