Finite Group DatabasebetaFinite Group DatabasebetaOrder 33344.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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. #30659754 | C2 | semidirect |
| 2. #30659739 | C2 | semidirect |
| 3. #30659733 | C2 | semidirect |
| 4. #30659728 | C2 | semidirect |
| 5. C2×#22552351 | C2 | semidirect |
| 6. #30659715 | C2 | semidirect |
| 7. 2−1+4×C521 | C2 | semidirect |
| 12. #22552354 | C22 | semidirect |
| 13. #22552352 | C22 | semidirect |
| 14. #22552351 | C22 | semidirect |
| 15. #22552351 | C22 | semidirect |
| 16. #22552349 | C22 | semidirect |
| 17. #22552348 | C22 | semidirect |
| 18. C2×#16861960 | C22 | semidirect |
| 21. #41×C521 | C22 | semidirect |
| 23. C2×Q8×C521 | C22 | semidirect |
| 53. C521 | #577 | semidirect |
| 55. 2−1+4 | D521 | semidirect |
| 66. #41 | C2×D521 | semidirect |
| 68. C2×Q8 | C2×D521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30659754 | 2 |
| #30659739 | 2 |
| #30659733 | 2 |
| #30659728 | 2 |
| C2×#22552351 | 2 |
| #30659715 | 2 |
| 2−1+4×C521 | 2 |
| #577 | 521 |