Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
300 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 3. #23758238 | C2 | semidirect |
| 4. C2×C8×#10597845 | C2 | semidirect |
| 5. #23758149 | C2 | semidirect |
| 6. #23758143 | C2 | semidirect |
| 9. #19097858 | C4 | semidirect |
| 16. #19097835 | C4 | semidirect |
| 23. #19097696 | C4 | semidirect |
| 24. #19097694 | C4 | semidirect |
| 25. #19097692 | C4 | semidirect |
| 26. #102×C157 | C4 | semidirect |
| 109. C157 | #1764 | semidirect |
| 133. #102 | #10597845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097858 | 2 |
| C2×#19097835 | 2 |
| #23758238 | 2 |
| C2×C8×#10597845 | 2 |
| #23758149 | 2 |
| #23758143 | 2 |
| #23757266 | 2 |
| #1764 | 157 |