Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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. C4×#14578954 | C2 | semidirect |
| 3. #23757386 | C2 | semidirect |
| 4. #23757381 | C2 | semidirect |
| 5. #23757375 | C2 | semidirect |
| 6. #23757311 | C2 | semidirect |
| 7. #23757270 | C2 | semidirect |
| 8. C2×#97×C157 | C2 | semidirect |
| 10. #19097793 | C4 | semidirect |
| 30. #14578954 | C2×C4 | semidirect |
| 36. Dic628 | C2×C4 | semidirect |
| 37. #14578943 | C2×C4 | semidirect |
| 38. D1256 | C2×C4 | semidirect |
| 48. C2×C8×C157 | C2×C4 | semidirect |
| 89. C157 | #2943 | semidirect |
| 98. C2×#97 | D157 | semidirect |
| 132. C2×C8 | C4×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097793 | 2 |
| C4×#14578954 | 2 |
| #23757386 | 2 |
| #23757381 | 2 |
| #23757375 | 2 |
| #23757311 | 2 |
| #23757270 | 2 |
| C2×#97×C157 | 2 |
| #2943 | 157 |