Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
198 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 69 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. #23782070 | C2 | semidirect |
| 2. #23782063 | C2 | semidirect |
| 5. #23782016 | C2 | semidirect |
| 7. #322×C163 | C2 | semidirect |
| 54. C8×C163 | SD16 | semidirect |
| 69. C163 | #1714 | semidirect |
| 77. #322 | D163 | semidirect |
| 124. C8 | #14579688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782070 | 2 |
| #23782063 | 2 |
| #23782038 | 2 |
| #23782016 | 2 |
| #23782012 | 2 |
| #322×C163 | 2 |
| #1714 | 163 |