Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
500 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 2. C4×#14579699 | C2 | semidirect |
| 3. C4×Dic652 | C2 | semidirect |
| 4. C4×#14579688 | C2 | semidirect |
| 5. C4×D1304 | C2 | semidirect |
| 6. #23781703 | C2 | semidirect |
| 7. #23781662 | C2 | semidirect |
| 8. C2×C4×C8×C163 | C2 | semidirect |
| 10. #19104757 | C4 | direct (N × H) |
| 30. #14579699 | C2×C4 | semidirect |
| 36. Dic652 | C2×C4 | semidirect |
| 37. #14579688 | C2×C4 | semidirect |
| 38. D1304 | C2×C4 | semidirect |
| 48. C2×C8×C163 | C2×C4 | semidirect |
| 83. C4×C163 | #135 | semidirect |
| 92. C163 | C4×#135 | semidirect |
| 101. C2×C4×C8 | D163 | semidirect |
| 135. C2×C8 | C4×D163 | semidirect |
| 178. C4 | #19104757 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104757 | 2 |
| C4×#14579699 | 2 |
| C4×Dic652 | 2 |
| C4×#14579688 | 2 |
| C4×D1304 | 2 |
| #23781703 | 2 |
| #23781662 | 2 |
| C2×C4×C8×C163 | 2 |
| C4×#135 | 163 |