Finite Group DatabasebetaFinite Group DatabasebetaOrder 3008.
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×D47 | C2 | semidirect |
| 3. #13094057 | C2 | semidirect |
| 4. #13094056 | C2 | semidirect |
| 5. #13094055 | C2 | semidirect |
| 6. #13094054 | C2 | semidirect |
| 7. #13094053 | C2 | semidirect |
| 8. Q16×D47 | C2 | semidirect |
| 9. SD16×D47 | C2 | semidirect |
| 10. M16×D47 | C2 | semidirect |
| 11. #137×C47 | C2 | semidirect |
| 13. C2×Q8×C47 | C22 | semidirect |
| 19. Q8×D47 | C22 | semidirect |
| 30. C2×Dic94 | C22 | semidirect |
| 31. Q16×C47 | C22 | semidirect |
| 32. SD16×C47 | C22 | semidirect |
| 33. M16×C47 | C22 | semidirect |
| 34. #10625337 | C22 | semidirect |
| 35. #10625337 | C22 | semidirect |
| 36. #10625336 | C22 | semidirect |
| 37. #10625335 | C22 | semidirect |
| 38. #10625329 | C22 | semidirect |
| 39. Dic188 | C22 | semidirect |
| 40. #10625325 | C22 | semidirect |
| 41. #10625324 | C22 | semidirect |
| 98. D47 | #137 | direct (N × H) |
| 100. C47 | C2×#137 | semidirect |
| 108. #137 | D47 | direct (N × H) |
| 125. C2×Q8 | C2×D47 | semidirect |
| 134. Q16 | C2×D47 | semidirect |
| 138. SD16 | C2×D47 | semidirect |
| 141. M16 | C2×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D47 | 2 |
| C2×Q8×D47 | 2 |
| #13094057 | 2 |
| #13094056 | 2 |
| #13094055 | 2 |
| #13094054 | 2 |
| #13094053 | 2 |
| Q16×D47 | 2 |
| SD16×D47 | 2 |
| M16×D47 | 2 |
| #137×C47 | 2 |
| C2×#137 | 47 |