Finite Group DatabasebetaFinite Group DatabasebetaOrder 33344.
104 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 2. #30659714 | C2 | semidirect |
| 3. #30659643 | C2 | semidirect |
| 4. #30659635 | C2 | semidirect |
| 5. #30659634 | C2 | semidirect |
| 6. #30659618 | C2 | semidirect |
| 7. #131×C521 | C2 | semidirect |
| 9. #22552354 | C4 | semidirect |
| 10. #22552352 | C4 | semidirect |
| 11. #22552351 | C4 | semidirect |
| 12. #22552349 | C4 | semidirect |
| 51. C521 | #444 | semidirect |
| 55. #131 | D521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30659728 | 2 |
| #30659714 | 2 |
| #30659643 | 2 |
| #30659635 | 2 |
| #30659634 | 2 |
| #30659618 | 2 |
| #131×C521 | 2 |
| #444 | 521 |