Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 135 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. C2×#11745311 | C2 | semidirect |
| 2. C2×M16×D29 | C2 | semidirect |
| 3. #14271670 | C2 | semidirect |
| 4. C2×#11745257 | C2 | semidirect |
| 5. #14271415 | C2 | semidirect |
| 6. #14271412 | C2 | semidirect |
| 7. #14271398 | C2 | semidirect |
| 8. #14271395 | C2 | semidirect |
| 9. #14271203 | C2 | semidirect |
| 10. #14271169 | C2 | semidirect |
| 11. C29×#417 | C2 | semidirect |
| 19. #11745308 | C22 | semidirect |
| 20. #11745308 | C22 | semidirect |
| 21. C2×#90784 | C22 | semidirect |
| 22. #11745300 | C22 | semidirect |
| 23. #11745300 | C22 | semidirect |
| 26. C2×#90782 | C22 | semidirect |
| 33. C2×#90772 | C22 | semidirect |
| 34. C2×C8×D29 | C22 | semidirect |
| 39. C29×#103 | C22 | semidirect |
| 40. C29×#102 | C22 | semidirect |
| 41. #11745169 | C22 | semidirect |
| 42. #11745169 | C22 | semidirect |
| 43. #11745156 | C22 | semidirect |
| 44. #11745155 | C22 | semidirect |
| 89. #90777 | D4 | semidirect |
| 136. #6597 | C2×D4 | semidirect |
| 155. C2×D29 | AGL(1,ℤ/8) | semidirect |
| 175. #417 | D29 | semidirect |
| 213. #103 | C2×D29 | semidirect |
| 216. #102 | C2×D29 | semidirect |
| 217. C29 | #3055 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745311 | 2 |
| C2×M16×D29 | 2 |
| #14271670 | 2 |
| C2×#11745257 | 2 |
| #14271415 | 2 |
| #14271412 | 2 |
| #14271398 | 2 |
| #14271395 | 2 |
| #14271203 | 2 |
| #14271169 | 2 |
| C29×#417 | 2 |
| #3055 | 29 |