Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14271971 | C2 | semidirect |
| 2. #14271965 | C2 | semidirect |
| 3. #14271548 | C2 | semidirect |
| 4. #14271435 | C2 | semidirect |
| 5. #14271433 | C2 | semidirect |
| 6. #14271428 | C2 | semidirect |
| 7. #14271339 | C2 | semidirect |
| 8. #14271336 | C2 | semidirect |
| 9. #14271280 | C2 | semidirect |
| 10. #14271278 | C2 | semidirect |
| 11. C29×#578 | C2 | semidirect |
| 12. C29×2−1+4 | C22 | semidirect |
| 15. C29×#137 | C22 | semidirect |
| 19. C2×Q16×C29 | C22 | semidirect |
| 20. C29×#131 | C22 | semidirect |
| 25. #11745311 | C22 | semidirect |
| 26. #11745310 | C22 | semidirect |
| 27. #11745309 | C22 | semidirect |
| 31. C2×#90784 | C22 | semidirect |
| 37. #11745185 | C22 | semidirect |
| 38. #11745185 | C22 | semidirect |
| 39. #11745184 | C22 | semidirect |
| 41. #11745171 | C22 | semidirect |
| 42. #11745170 | C22 | semidirect |
| 43. #11745167 | C22 | semidirect |
| 44. C8×Dic29 | C22 | semidirect |
| 144. #578 | D29 | semidirect |
| 161. 2−1+4 | C2×D29 | semidirect |
| 166. #137 | C2×D29 | semidirect |
| 177. C2×Q16 | C2×D29 | semidirect |
| 184. #131 | C2×D29 | semidirect |
| 194. C29 | #3290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271971 | 2 |
| #14271965 | 2 |
| #14271548 | 2 |
| #14271435 | 2 |
| #14271433 | 2 |
| #14271428 | 2 |
| #14271339 | 2 |
| #14271336 | 2 |
| #14271280 | 2 |
| #14271278 | 2 |
| C29×#578 | 2 |
| #3290 | 29 |