Finite Group DatabasebetaFinite Group DatabasebetaOrder 33344.
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. #30659703 | C2 | semidirect |
| 2. #30659701 | C2 | semidirect |
| 3. #30659698 | C2 | semidirect |
| 4. #30659694 | C2 | semidirect |
| 5. #30659692 | C2 | semidirect |
| 6. #30659689 | C2 | semidirect |
| 7. #30659685 | C2 | semidirect |
| 9. C4×Dic1042 | C2 | semidirect |
| 10. C4×C22⋊D521 | C2 | semidirect |
| 11. C4×C22⋊D521 | C2 | semidirect |
| 12. #30659667 | C2 | semidirect |
| 13. #30659665 | C2 | semidirect |
| 14. C2×C4×Dic521 | C2 | semidirect |
| 15. C4×D4×C521 | C2 | semidirect |
| 103. C521 | #529 | semidirect |
| 116. C4×D4 | D521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30659703 | 2 |
| #30659701 | 2 |
| #30659698 | 2 |
| #30659694 | 2 |
| #30659692 | 2 |
| #30659689 | 2 |
| #30659685 | 2 |
| #30659680 | 2 |
| C4×Dic1042 | 2 |
| C4×C22⋊D521 | 2 |
| #30659667 | 2 |
| #30659665 | 2 |
| C2×C4×Dic521 | 2 |
| C4×D4×C521 | 2 |
| #529 | 521 |