Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
244 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 65 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. #23782218 | C2 | semidirect |
| 4. #23781436 | C2 | semidirect |
| 5. #23781426 | C2 | semidirect |
| 6. #23781421 | C2 | semidirect |
| 44. C2×Q8×C163 | Q8 | semidirect |
| 46. C2×D4×C163 | Q8 | semidirect |
| 102. C163 | #2031 | semidirect |
| 131. C2×Q8 | Dic326 | semidirect |
| 133. C2×D4 | Dic326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782218 | 2 |
| C2×#19104662 | 2 |
| #23781639 | 2 |
| #23781436 | 2 |
| #23781426 | 2 |
| #23781421 | 2 |
| #421×C163 | 2 |
| #2031 | 163 |