Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 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. #23782045 | C2 | semidirect |
| 4. #23781410 | C2 | semidirect |
| 5. #335×C163 | C2 | semidirect |
| 36. D652 | Q16 | semidirect |
| 63. C163 | #1669 | semidirect |
| 68. #335 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782045 | 2 |
| #23781946 | 2 |
| C8×D652 | 2 |
| #23781410 | 2 |
| #335×C163 | 2 |
| #1669 | 163 |