Finite Group DatabasebetaFinite Group DatabasebetaOrder 3392.
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×D53 | C2 | semidirect |
| 3. #13133250 | C2 | semidirect |
| 4. #13133249 | C2 | semidirect |
| 5. #13133248 | C2 | semidirect |
| 6. #13133247 | C2 | semidirect |
| 7. #13133246 | C2 | semidirect |
| 8. Q16×D53 | C2 | semidirect |
| 9. SD16×D53 | C2 | semidirect |
| 10. M16×D53 | C2 | semidirect |
| 11. #137×C53 | C2 | semidirect |
| 13. C2×Q8×C53 | C22 | semidirect |
| 19. Q8×D53 | C22 | semidirect |
| 30. C2×Dic106 | C22 | semidirect |
| 31. Q16×C53 | C22 | semidirect |
| 32. SD16×C53 | C22 | semidirect |
| 33. M16×C53 | C22 | semidirect |
| 34. #11719925 | C22 | semidirect |
| 35. #11719925 | C22 | semidirect |
| 36. #11719924 | C22 | semidirect |
| 37. #11719923 | C22 | semidirect |
| 38. #11719917 | C22 | semidirect |
| 39. Dic212 | C22 | semidirect |
| 40. #11719913 | C22 | semidirect |
| 41. #11719912 | C22 | semidirect |
| 98. D53 | #137 | direct (N × H) |
| 100. C53 | C2×#137 | semidirect |
| 108. #137 | D53 | direct (N × H) |
| 125. C2×Q8 | C2×D53 | semidirect |
| 134. Q16 | C2×D53 | semidirect |
| 138. SD16 | C2×D53 | semidirect |
| 141. M16 | C2×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D53 | 2 |
| C2×Q8×D53 | 2 |
| #13133250 | 2 |
| #13133249 | 2 |
| #13133248 | 2 |
| #13133247 | 2 |
| #13133246 | 2 |
| Q16×D53 | 2 |
| SD16×D53 | 2 |
| M16×D53 | 2 |
| #137×C53 | 2 |
| C2×#137 | 53 |