Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 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. #14271965 | C2 | semidirect |
| 2. #14271600 | C2 | semidirect |
| 3. #14271598 | C2 | semidirect |
| 4. #14271596 | C2 | semidirect |
| 5. C2×D464 | C2 | semidirect |
| 6. D16×D29 | C2 | semidirect |
| 7. #14271579 | C2 | semidirect |
| 8. C29×#508 | C2 | semidirect |
| 10. C29×#135 | C22 | semidirect |
| 12. #11745281 | C22 | semidirect |
| 14. D8×D29 | C22 | semidirect |
| 15. C2×D232 | C22 | semidirect |
| 17. C29×Q32 | C22 | semidirect |
| 18. C29×SD32 | C22 | semidirect |
| 19. C29×D16 | C22 | semidirect |
| 20. C2×C16×C29 | C22 | semidirect |
| 21. #11745176 | C22 | semidirect |
| 22. #11745174 | C22 | semidirect |
| 23. #11745160 | C22 | semidirect |
| 24. D464 | C22 | semidirect |
| 25. D464 | C22 | semidirect |
| 26. #11745146 | C22 | semidirect |
| 27. C16×D29 | C22 | semidirect |
| 84. #508 | D29 | semidirect |
| 97. #135 | C2×D29 | semidirect |
| 101. Q32 | C2×D29 | semidirect |
| 103. SD32 | C2×D29 | semidirect |
| 107. D16 | C2×D29 | semidirect |
| 111. C2×C16 | C2×D29 | semidirect |
| 112. C29 | #3415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271965 | 2 |
| #14271600 | 2 |
| #14271598 | 2 |
| #14271596 | 2 |
| C2×D464 | 2 |
| D16×D29 | 2 |
| #14271579 | 2 |
| C29×#508 | 2 |
| #3415 | 29 |