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×#11745304 | C2 | semidirect |
| 2. C2×#11745294 | C2 | semidirect |
| 3. C2×#11745266 | C2 | semidirect |
| 4. #14271737 | C2 | semidirect |
| 5. #14271730 | C2 | semidirect |
| 6. #14271554 | C2 | semidirect |
| 7. #14271549 | C2 | semidirect |
| 8. #14271544 | C2 | semidirect |
| 9. #14271534 | C2 | semidirect |
| 10. #14271118 | C2 | semidirect |
| 11. C22×SD16×C29 | C2 | semidirect |
| 21. #11745309 | C22 | semidirect |
| 23. #11745306 | C22 | semidirect |
| 24. C2×#90785 | C22 | semidirect |
| 26. C2×#90784 | C22 | semidirect |
| 36. C2×Dic116 | C22 | semidirect |
| 38. C2×D232 | C22 | semidirect |
| 39. C2×#90773 | C22 | semidirect |
| 40. C2×#90773 | C22 | semidirect |
| 41. #11745163 | C22 | semidirect |
| 42. C8×Dic29 | C22 | semidirect |
| 69. C2×C8×C29 | D4 | semidirect |
| 82. #90777 | D4 | semidirect |
| 146. C22×SD16 | D29 | semidirect |
| 191. C29 | #3154 | semidirect |
| 228. C2×C8 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745304 | 2 |
| C2×#11745294 | 2 |
| C2×#11745266 | 2 |
| #14271737 | 2 |
| #14271730 | 2 |
| #14271554 | 2 |
| #14271549 | 2 |
| #14271544 | 2 |
| #14271534 | 2 |
| #14271118 | 2 |
| C22×SD16×C29 | 2 |
| #3154 | 29 |