Finite Group DatabasebetaFinite Group DatabasebetaOrder 33344.
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. #30659706 | C2 | semidirect |
| 2. #30659698 | C2 | semidirect |
| 3. #30659698 | C2 | semidirect |
| 4. #30659686 | C2 | semidirect |
| 5. #30659686 | C2 | semidirect |
| 6. #30659685 | C2 | semidirect |
| 7. #30659685 | C2 | semidirect |
| 8. #30659684 | C2 | semidirect |
| 9. #30659673 | C2 | semidirect |
| 13. C2×#22552343 | C2 | semidirect |
| 14. C4⋊C4×D521 | C2 | semidirect |
| 15. C22⋊Q8×C521 | C2 | semidirect |
| 54. C22⋊D521 | Q8 | semidirect |
| 101. C521 | #554 | semidirect |
| 111. C22⋊Q8 | D521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30659706 | 2 |
| #30659698 | 2 |
| #30659686 | 2 |
| #30659685 | 2 |
| #30659684 | 2 |
| #30659673 | 2 |
| C4×C22⋊D521 | 2 |
| #30659668 | 2 |
| C2×#22552343 | 2 |
| C4⋊C4×D521 | 2 |
| C22⋊Q8×C521 | 2 |
| #554 | 521 |