Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 1. C2×#19097793 | C2 | semidirect |
| 2. C2×#19097791 | C2 | semidirect |
| 3. #23757819 | C2 | semidirect |
| 4. #23757666 | C2 | semidirect |
| 5. #23757664 | C2 | semidirect |
| 6. #23757661 | C2 | semidirect |
| 7. #23757659 | C2 | semidirect |
| 8. C2×#19097681 | C2 | semidirect |
| 9. C2×#135×C157 | C2 | semidirect |
| 51. C2×#11929434 | D4 | semidirect |
| 68. C2×C8×C157 | D4 | semidirect |
| 116. C157 | #3150 | semidirect |
| 120. C2×#135 | D157 | semidirect |
| 180. C2×C8 | C22⋊D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097793 | 2 |
| C2×#19097791 | 2 |
| #23757819 | 2 |
| #23757666 | 2 |
| #23757664 | 2 |
| #23757661 | 2 |
| #23757659 | 2 |
| C2×#19097681 | 2 |
| C2×#135×C157 | 2 |
| #3150 | 157 |