Finite Group DatabasebetaFinite Group DatabasebetaOrder 20032.
212 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 97 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. #23756496 | C2 | semidirect |
| 2. #23756492 | C2 | semidirect |
| 3. #23756490 | C2 | semidirect |
| 5. #23756473 | C2 | semidirect |
| 6. Q8×Dic313 | C2 | semidirect |
| 7. #23756462 | C2 | semidirect |
| 9. #23756456 | C2 | semidirect |
| 10. #23756455 | C2 | semidirect |
| 11. C22⋊Q8×C313 | C2 | semidirect |
| 72. C313 | #556 | semidirect |
| 79. C22⋊Q8 | D313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23756496 | 2 |
| #23756492 | 2 |
| #23756490 | 2 |
| #23756483 | 2 |
| #23756473 | 2 |
| Q8×Dic313 | 2 |
| #23756462 | 2 |
| C4×C22⋊D313 | 2 |
| #23756456 | 2 |
| #23756455 | 2 |
| C22⋊Q8×C313 | 2 |
| #556 | 313 |