Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
184 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 3. #23781416 | C2 | semidirect |
| 4. #23781415 | C2 | semidirect |
| 5. #334×C163 | C2 | semidirect |
| 43. C163⋊C8 | M16 | semidirect |
| 49. C8×C163 | M16 | semidirect |
| 65. C163 | #1566 | semidirect |
| 71. #334 | D163 | semidirect |
| 115. C8 | #14579682 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781687 | 2 |
| C4×C8×D163 | 2 |
| #23781416 | 2 |
| #23781415 | 2 |
| #334×C163 | 2 |
| #1566 | 163 |