Finite Group DatabasebetaFinite Group DatabasebetaOrder 20032.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #23756492 | C2 | semidirect |
| 2. #23756488 | C2 | semidirect |
| 3. #23756486 | C2 | semidirect |
| 4. #23756481 | C2 | semidirect |
| 6. Q8×Dic313 | C2 | semidirect |
| 7. #23756459 | C2 | semidirect |
| 8. #23756457 | C2 | semidirect |
| 9. #23756455 | C2 | semidirect |
| 10. C2×C4×Dic313 | C2 | semidirect |
| 11. C22⋊Q8×C313 | C2 | semidirect |
| 74. C313 | #529 | semidirect |
| 80. C22⋊Q8 | D313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23756492 | 2 |
| #23756488 | 2 |
| #23756486 | 2 |
| #23756481 | 2 |
| #23756471 | 2 |
| Q8×Dic313 | 2 |
| #23756459 | 2 |
| #23756457 | 2 |
| #23756455 | 2 |
| C2×C4×Dic313 | 2 |
| C22⋊Q8×C313 | 2 |
| #529 | 313 |