Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19097801 | C2 | semidirect |
| 2. C22×#14578942 | C2 | semidirect |
| 3. #23757750 | C2 | semidirect |
| 4. #23757492 | C2 | semidirect |
| 5. #23757470 | C2 | semidirect |
| 6. #23757300 | C2 | semidirect |
| 7. #23757278 | C2 | semidirect |
| 8. #23757269 | C2 | semidirect |
| 12. C2×#14578944 | C22 | semidirect |
| 15. C2×#14578942 | C22 | semidirect |
| 18. C4×Dic314 | C22 | semidirect |
| 22. C4⋊#11929434 | C22 | semidirect |
| 23. #19097695 | C22 | semidirect |
| 25. #19097692 | C22 | semidirect |
| 35. C2×Dic314 | D4 | semidirect |
| 116. C157 | #3043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097801 | 2 |
| C22×#14578942 | 2 |
| #23757750 | 2 |
| #23757492 | 2 |
| #23757470 | 2 |
| #23757300 | 2 |
| #23757278 | 2 |
| #23757269 | 2 |
| #535×C157 | 2 |
| #3043 | 157 |