Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
492 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 175 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×#14579700 | C2 | semidirect |
| 3. #23781778 | C2 | semidirect |
| 4. #23781776 | C2 | semidirect |
| 5. #23781772 | C2 | semidirect |
| 6. #23781768 | C2 | semidirect |
| 7. #23781763 | C2 | semidirect |
| 8. #23781700 | C2 | semidirect |
| 9. #23781660 | C2 | semidirect |
| 10. #97×D163 | C2 | semidirect |
| 11. #441×C163 | C2 | semidirect |
| 13. #19104758 | C4 | semidirect |
| 41. #14579700 | C2×C4 | semidirect |
| 49. #14579686 | C2×C4 | semidirect |
| 50. D1304 | C2×C4 | semidirect |
| 54. C8×D163 | C2×C4 | semidirect |
| 65. Q16×C163 | C2×C4 | semidirect |
| 114. C163 | #2943 | semidirect |
| 121. #441 | D163 | semidirect |
| 165. Q16 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104758 | 2 |
| C4×#14579700 | 2 |
| #23781778 | 2 |
| #23781776 | 2 |
| #23781772 | 2 |
| #23781768 | 2 |
| #23781763 | 2 |
| #23781700 | 2 |
| #23781660 | 2 |
| #97×D163 | 2 |
| #441×C163 | 2 |
| #2943 | 163 |