Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
292 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23757231 | C2 | semidirect |
| 4. C2×#19097682 | C2 | semidirect |
| 5. #23757037 | C2 | semidirect |
| 6. #23757033 | C2 | semidirect |
| 9. #19097778 | C4 | semidirect |
| 16. #19097695 | C4 | semidirect |
| 17. #19097692 | C4 | semidirect |
| 24. #104×C157 | C4 | semidirect |
| 98. C157 | #1765 | semidirect |
| 118. #104 | Dic157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097778 | 2 |
| #23757269 | 2 |
| #23757231 | 2 |
| C2×#19097682 | 2 |
| #23757037 | 2 |
| #23757033 | 2 |
| C2×#104×C157 | 2 |
| #1765 | 157 |