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. #30659699 | C2 | semidirect |
| 3. #30659697 | C2 | semidirect |
| 4. #30659692 | C2 | semidirect |
| 6. Q8×Dic521 | C2 | semidirect |
| 7. #30659670 | C2 | semidirect |
| 8. #30659668 | C2 | semidirect |
| 9. #30659666 | C2 | semidirect |
| 10. C2×C4×Dic521 | C2 | semidirect |
| 11. C22⋊Q8×C521 | C2 | semidirect |
| 74. C521 | #529 | semidirect |
| 80. C22⋊Q8 | D521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30659703 | 2 |
| #30659699 | 2 |
| #30659697 | 2 |
| #30659692 | 2 |
| #30659682 | 2 |
| Q8×Dic521 | 2 |
| #30659670 | 2 |
| #30659668 | 2 |
| #30659666 | 2 |
| C2×C4×Dic521 | 2 |
| C22⋊Q8×C521 | 2 |
| #529 | 521 |