Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
212 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 4. #23781407 | C2 | semidirect |
| 5. #23781406 | C2 | semidirect |
| 6. #23781406 | C2 | semidirect |
| 7. #330×C163 | C2 | semidirect |
| 93. C163 | #1531 | semidirect |
| 101. #330 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782221 | 2 |
| #23781720 | 2 |
| #97×D163 | 2 |
| #23781407 | 2 |
| #23781406 | 2 |
| #330×C163 | 2 |
| #1531 | 163 |