Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11745313 | C2 | semidirect |
| 2. C2×#11745294 | C2 | semidirect |
| 3. C2×#11745312 | C2 | semidirect |
| 4. C22×#90783 | C2 | semidirect |
| 5. #14271739 | C2 | semidirect |
| 6. #14271558 | C2 | semidirect |
| 7. #14271550 | C2 | semidirect |
| 8. #14271545 | C2 | semidirect |
| 9. #14271535 | C2 | semidirect |
| 10. #14271119 | C2 | semidirect |
| 11. C29×#535 | C2 | semidirect |
| 23. C2×#90785 | C22 | semidirect |
| 24. C2×#90785 | C22 | semidirect |
| 25. C2×#90784 | C22 | semidirect |
| 30. C2×#90783 | C22 | semidirect |
| 31. C2×#90783 | C22 | semidirect |
| 34. C2×#90782 | C22 | semidirect |
| 39. #11745237 | C22 | semidirect |
| 40. #11745231 | C22 | semidirect |
| 41. #11745151 | C22 | semidirect |
| 42. C4×#6597 | C22 | semidirect |
| 83. #90777 | D4 | semidirect |
| 84. C2×#6597 | D4 | semidirect |
| 148. #535 | D29 | semidirect |
| 191. C29 | #3154 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745313 | 2 |
| C2×#11745294 | 2 |
| C2×#11745312 | 2 |
| C22×#90783 | 2 |
| #14271739 | 2 |
| #14271558 | 2 |
| #14271550 | 2 |
| #14271545 | 2 |
| #14271535 | 2 |
| #14271119 | 2 |
| C29×#535 | 2 |
| #3154 | 29 |