Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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. #14271873 | C2 | semidirect |
| 3. #14271509 | C2 | semidirect |
| 4. #14271480 | C2 | semidirect |
| 5. #14271454 | C2 | semidirect |
| 6. #14271389 | C2 | semidirect |
| 7. #14271312 | C2 | semidirect |
| 8. C4×#90784 | C2 | semidirect |
| 9. #14271228 | C2 | semidirect |
| 10. #102×D29 | C2 | semidirect |
| 11. C29×#460 | C2 | semidirect |
| 14. C2×SD16×C29 | C22 | semidirect |
| 16. C4×Q8×C29 | C22 | semidirect |
| 17. #11745308 | C22 | semidirect |
| 22. C2×C8×D29 | C22 | semidirect |
| 24. C4⋊C4×D29 | C22 | semidirect |
| 29. #11745231 | C22 | semidirect |
| 30. C29×C4⋊C8 | C22 | semidirect |
| 31. C29×#102 | C22 | semidirect |
| 32. #11745183 | C22 | semidirect |
| 33. #11745180 | C22 | semidirect |
| 34. #11745180 | C22 | semidirect |
| 36. #11745168 | C22 | semidirect |
| 37. #11745165 | C22 | semidirect |
| 39. #11745156 | C22 | semidirect |
| 40. C4×#6597 | C22 | semidirect |
| 100. D116 | SD16 | semidirect |
| 137. #460 | D29 | semidirect |
| 151. C2×SD16 | C2×D29 | semidirect |
| 161. C4×Q8 | C2×D29 | semidirect |
| 168. C4⋊C8 | C2×D29 | semidirect |
| 174. #102 | C2×D29 | semidirect |
| 177. C29 | #3295 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271873 | 2 |
| #14271798 | 2 |
| #14271509 | 2 |
| #14271480 | 2 |
| #14271454 | 2 |
| #14271389 | 2 |
| #14271312 | 2 |
| C4×#90784 | 2 |
| #14271228 | 2 |
| #102×D29 | 2 |
| C29×#460 | 2 |
| #3295 | 29 |