Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
484 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 175 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. #23757752 | C2 | semidirect |
| 3. #23757385 | C2 | semidirect |
| 4. #23757381 | C2 | semidirect |
| 5. #23757379 | C2 | semidirect |
| 6. #23757364 | C2 | semidirect |
| 7. C4×#14578942 | C2 | semidirect |
| 8. #106×D157 | C2 | semidirect |
| 9. #23757271 | C2 | semidirect |
| 10. #23757230 | C2 | semidirect |
| 11. #442×C157 | C2 | semidirect |
| 13. #19097790 | C4 | semidirect |
| 41. #14578953 | C2×C4 | semidirect |
| 48. Dic628 | C2×C4 | semidirect |
| 49. #14578942 | C2×C4 | semidirect |
| 53. C8×D157 | C2×C4 | semidirect |
| 66. D8×C157 | C2×C4 | semidirect |
| 114. C157 | #2952 | semidirect |
| 119. #442 | D157 | semidirect |
| 167. D8 | C4×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097790 | 2 |
| #23757752 | 2 |
| #23757385 | 2 |
| #23757381 | 2 |
| #23757379 | 2 |
| #23757364 | 2 |
| C4×#14578942 | 2 |
| #106×D157 | 2 |
| #23757271 | 2 |
| #23757230 | 2 |
| #442×C157 | 2 |
| #2952 | 157 |