Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
596 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 137 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×#11745273 | C2 | semidirect |
| 2. C2×#11745274 | C2 | semidirect |
| 3. C2×D8×D29 | C2 | semidirect |
| 4. #14271726 | C2 | semidirect |
| 5. #14271551 | C2 | semidirect |
| 6. #14271550 | C2 | semidirect |
| 7. #14271547 | C2 | semidirect |
| 8. #14271546 | C2 | semidirect |
| 9. #14271538 | C2 | semidirect |
| 10. #14271117 | C2 | semidirect |
| 11. C29×#493 | C2 | semidirect |
| 15. C2×D8×C29 | C22 | semidirect |
| 16. C2×D8×C29 | C22 | semidirect |
| 17. C29×#127 | C22 | semidirect |
| 18. #11745302 | C22 | semidirect |
| 21. #11745298 | C22 | semidirect |
| 22. C2×#90783 | C22 | semidirect |
| 23. C2×#90783 | C22 | semidirect |
| 25. C2×#90782 | C22 | semidirect |
| 29. C2×Dic116 | C22 | semidirect |
| 31. C2×#90773 | C22 | semidirect |
| 34. #11745237 | C22 | semidirect |
| 36. C4×C8×C29 | C22 | semidirect |
| 37. #11745163 | C22 | semidirect |
| 38. C8×Dic29 | C22 | semidirect |
| 39. #11745151 | C22 | semidirect |
| 75. #90772 | D4 | semidirect |
| 76. C8×D29 | D4 | semidirect |
| 133. #493 | D29 | semidirect |
| 154. C2×D8 | C2×D29 | semidirect |
| 155. C2×D8 | C2×D29 | semidirect |
| 159. #127 | C2×D29 | semidirect |
| 168. C4×C8 | C2×D29 | semidirect |
| 169. C29 | #3155 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745273 | 2 |
| C2×#11745274 | 2 |
| C2×D8×D29 | 2 |
| #14271726 | 2 |
| #14271551 | 2 |
| #14271550 | 2 |
| #14271547 | 2 |
| #14271546 | 2 |
| #14271538 | 2 |
| #14271117 | 2 |
| C29×#493 | 2 |
| #3155 | 29 |