Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
500 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 185 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. #23782133 | C2 | semidirect |
| 3. #23781759 | C2 | semidirect |
| 4. #23781752 | C2 | semidirect |
| 5. #23781747 | C2 | semidirect |
| 6. #23781659 | C2 | semidirect |
| 7. C2×C8×Dic163 | C2 | semidirect |
| 8. #427×C163 | C2 | semidirect |
| 10. #19104757 | C4 | semidirect |
| 30. #14579699 | C2×C4 | semidirect |
| 37. Dic652 | C2×C4 | semidirect |
| 38. #14579688 | C2×C4 | semidirect |
| 39. D1304 | C2×C4 | semidirect |
| 49. C2×C8×C163 | C2×C4 | semidirect |
| 87. Dic163 | #135 | semidirect |
| 92. C163 | C4×#135 | semidirect |
| 99. #427 | D163 | semidirect |
| 136. C2×C8 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104757 | 2 |
| #23782133 | 2 |
| #23781759 | 2 |
| #23781752 | 2 |
| #23781747 | 2 |
| #23781659 | 2 |
| C2×C8×Dic163 | 2 |
| #427×C163 | 2 |
| C4×#135 | 163 |