Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
346 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23757748 | C2 | semidirect |
| 3. #23757289 | C2 | semidirect |
| 4. #23757246 | C2 | semidirect |
| 5. #23757045 | C2 | semidirect |
| 6. #23757029 | C2 | semidirect |
| 7. #418×C157 | C2 | semidirect |
| 11. C2×#14578942 | C4 | semidirect |
| 12. C2×#14578939 | C4 | semidirect |
| 29. C2×Dic314 | C2×C4 | semidirect |
| 30. C2×D628 | C2×C4 | semidirect |
| 38. C2×#11929434 | C2×C4 | semidirect |
| 115. C157 | #1904 | semidirect |
| 120. #418 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097797 | 2 |
| #23757748 | 2 |
| #23757289 | 2 |
| #23757246 | 2 |
| #23757045 | 2 |
| #23757029 | 2 |
| #418×C157 | 2 |
| #1904 | 157 |