Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
188 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 188 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. #23782039 | C2 | semidirect |
| 2. #23781942 | C2 | semidirect |
| 4. #23781730 | C2 | semidirect |
| 5. #23781415 | C2 | semidirect |
| 6. #23781408 | C2 | semidirect |
| 7. #332×C163 | C2 | semidirect |
| 51. D652 | SD16 | semidirect |
| 57. C163⋊C8 | D8 | semidirect |
| 85. C163 | #1665 | semidirect |
| 92. #332 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782039 | 2 |
| #23781942 | 2 |
| #23781861 | 2 |
| #23781730 | 2 |
| #23781415 | 2 |
| #23781408 | 2 |
| #332×C163 | 2 |
| #1665 | 163 |