Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
266 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 266 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. #23782296 | C2 | semidirect |
| 4. #23781403 | C2 | semidirect |
| 5. #324×C163 | C2 | semidirect |
| 63. C2×C4×C163 | SD16 | semidirect |
| 90. C163 | #1599 | semidirect |
| 96. #324 | D163 | semidirect |
| 154. C2×C4 | #14579688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782296 | 2 |
| #23781818 | 2 |
| #23781582 | 2 |
| #23781403 | 2 |
| #324×C163 | 2 |
| #1599 | 163 |