Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
206 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 45 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. #23782415 | C2 | semidirect |
| 3. #23782030 | C2 | semidirect |
| 4. #23781406 | C2 | semidirect |
| 5. #329×C163 | C2 | semidirect |
| 69. C163 | #1657 | semidirect |
| 75. #329 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782415 | 2 |
| #23782055 | 2 |
| #23782030 | 2 |
| #23781406 | 2 |
| #329×C163 | 2 |
| #1657 | 163 |