Finite Group DatabasebetaFinite Group DatabasebetaOrder 33344.
258 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 258 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 |
|---|---|---|
| 2. C2×Q8×D521 | C2 | semidirect |
| 3. #30659741 | C2 | semidirect |
| 4. #30659740 | C2 | semidirect |
| 5. #30659739 | C2 | semidirect |
| 6. #30659738 | C2 | semidirect |
| 7. #30659737 | C2 | semidirect |
| 8. Q16×D521 | C2 | semidirect |
| 9. SD16×D521 | C2 | semidirect |
| 10. M16×D521 | C2 | semidirect |
| 11. #137×C521 | C2 | semidirect |
| 18. C2×Dic1042 | C22 | semidirect |
| 23. Q8×D521 | C22 | semidirect |
| 29. Dic2084 | C22 | semidirect |
| 30. #22552354 | C22 | semidirect |
| 31. #22552354 | C22 | semidirect |
| 32. #22552353 | C22 | semidirect |
| 33. #22552352 | C22 | semidirect |
| 34. #22552351 | C22 | semidirect |
| 35. #22552348 | C22 | semidirect |
| 36. #22552347 | C22 | semidirect |
| 39. C2×Q8×C521 | C22 | semidirect |
| 40. Q16×C521 | C22 | semidirect |
| 41. SD16×C521 | C22 | semidirect |
| 42. M16×C521 | C22 | semidirect |
| 98. D521 | #137 | direct (N × H) |
| 99. C521 | C2×#137 | semidirect |
| 108. #137 | D521 | direct (N × H) |
| 125. C2×Q8 | C2×D521 | semidirect |
| 134. Q16 | C2×D521 | semidirect |
| 138. SD16 | C2×D521 | semidirect |
| 141. M16 | C2×D521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D521 | 2 |
| C2×Q8×D521 | 2 |
| #30659741 | 2 |
| #30659740 | 2 |
| #30659739 | 2 |
| #30659738 | 2 |
| #30659737 | 2 |
| Q16×D521 | 2 |
| SD16×D521 | 2 |
| M16×D521 | 2 |
| #137×C521 | 2 |
| C2×#137 | 521 |