Finite Group DatabasebetaFinite Group DatabasebetaOrder 20032.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23756491 | C2 | semidirect |
| 2. #23756489 | C2 | semidirect |
| 3. #23756485 | C2 | semidirect |
| 4. #23756480 | C2 | semidirect |
| 5. #23756476 | C2 | semidirect |
| 7. C4×Dic626 | C2 | semidirect |
| 8. C4×D1252 | C2 | semidirect |
| 9. C4×C22⋊D313 | C2 | semidirect |
| 10. #23756454 | C2 | semidirect |
| 11. C2×C42×C313 | C2 | semidirect |
| 74. C313 | #529 | semidirect |
| 86. C2×C42 | D313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23756491 | 2 |
| #23756489 | 2 |
| #23756485 | 2 |
| #23756480 | 2 |
| #23756476 | 2 |
| #23756471 | 2 |
| C4×Dic626 | 2 |
| C4×D1252 | 2 |
| C4×C22⋊D313 | 2 |
| #23756454 | 2 |
| C2×C42×C313 | 2 |
| #529 | 313 |