Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
166 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 57 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. #23782063 | C2 | semidirect |
| 5. #23781413 | C2 | semidirect |
| 6. #23781412 | C2 | semidirect |
| 7. #334×C163 | C2 | semidirect |
| 59. C8×C163 | SD16 | semidirect |
| 76. C163 | #1671 | semidirect |
| 82. #334 | D163 | semidirect |
| 136. C8 | #14579688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782063 | 2 |
| #23781956 | 2 |
| #23781871 | 2 |
| C8×D652 | 2 |
| #23781413 | 2 |
| #23781412 | 2 |
| #334×C163 | 2 |
| #1671 | 163 |