Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
140 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 47 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. #23781490 | C2 | semidirect |
| 4. #23781470 | C2 | semidirect |
| 5. #23781468 | C2 | semidirect |
| 7. #366×C163 | C2 | semidirect |
| 66. C163 | #2236 | semidirect |
| 71. #366 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781907 | 2 |
| #107×D163 | 2 |
| #23781490 | 2 |
| #23781470 | 2 |
| #23781468 | 2 |
| (C2×D163)⋊C16 | 2 |
| #366×C163 | 2 |
| #2236 | 163 |