Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
520 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 173 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. #23757180 | C2 | semidirect |
| 3. #23757164 | C2 | semidirect |
| 4. #23757162 | C2 | semidirect |
| 6. #23757147 | C2 | semidirect |
| 7. #23757144 | C2 | semidirect |
| 8. #23757137 | C2 | semidirect |
| 9. #391×C157 | C2 | semidirect |
| 12. #19097760 | C4 | semidirect |
| 48. #14578931 | C2×C4 | semidirect |
| 49. #14578931 | C2×C4 | semidirect |
| 51. C4×Dic157 | C2×C4 | semidirect |
| 54. C2×Q8×C157 | C2×C4 | semidirect |
| 123. C157 | #2379 | semidirect |
| 127. #391 | D157 | semidirect |
| 159. C2×Q8 | C4×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097760 | 2 |
| #23757180 | 2 |
| #23757164 | 2 |
| #23757162 | 2 |
| #23757151 | 2 |
| #23757147 | 2 |
| #23757144 | 2 |
| #23757137 | 2 |
| #391×C157 | 2 |
| #2379 | 157 |