Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
484 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 153 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. C2×#19104766 | C2 | semidirect |
| 3. #23781887 | C2 | semidirect |
| 4. #23781875 | C2 | semidirect |
| 5. #23781865 | C2 | semidirect |
| 6. #23781689 | C2 | semidirect |
| 7. #23781664 | C2 | semidirect |
| 8. C2×C4×Q8×C163 | C2 | semidirect |
| 52. C2×Q8×C163 | D4 | semidirect |
| 111. C4×C163 | #137 | semidirect |
| 120. C163 | #3037 | semidirect |
| 124. C2×C4×Q8 | D163 | semidirect |
| 160. C2×Q8 | D652 | semidirect |
| 233. C4 | #19104766 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104766 | 2 |
| #23782215 | 2 |
| #23781887 | 2 |
| #23781875 | 2 |
| #23781865 | 2 |
| #23781689 | 2 |
| #23781664 | 2 |
| C2×C4×Q8×C163 | 2 |
| #3037 | 163 |