Finite Group DatabasebetaFinite Group DatabasebetaOrder 20032.
228 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 105 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. #23756495 | C2 | semidirect |
| 2. #23756487 | C2 | semidirect |
| 3. #23756487 | C2 | semidirect |
| 4. #23756475 | C2 | semidirect |
| 5. #23756475 | C2 | semidirect |
| 6. #23756474 | C2 | semidirect |
| 7. #23756474 | C2 | semidirect |
| 8. #23756473 | C2 | semidirect |
| 9. #23756462 | C2 | semidirect |
| 13. C2×#19097540 | C2 | semidirect |
| 14. C4⋊C4×D313 | C2 | semidirect |
| 15. C22⋊Q8×C313 | C2 | semidirect |
| 54. C22⋊D313 | Q8 | semidirect |
| 101. C313 | #554 | semidirect |
| 111. C22⋊Q8 | D313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23756495 | 2 |
| #23756487 | 2 |
| #23756475 | 2 |
| #23756474 | 2 |
| #23756473 | 2 |
| #23756462 | 2 |
| C4×C22⋊D313 | 2 |
| #23756457 | 2 |
| C2×#19097540 | 2 |
| C4⋊C4×D313 | 2 |
| C22⋊Q8×C313 | 2 |
| #554 | 313 |