Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. #14271637 | C2 | semidirect |
| 3. #14271274 | C2 | semidirect |
| 4. #14271245 | C2 | semidirect |
| 5. #14271167 | C2 | semidirect |
| 6. #14271118 | C2 | semidirect |
| 7. C29×#427 | C2 | semidirect |
| 13. C2×D232 | C4 | semidirect |
| 16. #11745255 | C22 | semidirect |
| 19. C29×#107 | C22 | semidirect |
| 20. C29×#106 | C22 | semidirect |
| 21. #11745163 | C22 | semidirect |
| 22. C8×Dic29 | C22 | semidirect |
| 23. #11745157 | C22 | semidirect |
| 28. C2×D116 | C2×C4 | semidirect |
| 31. C2×C8×C29 | C2×C4 | semidirect |
| 43. D232 | C2×C4 | semidirect |
| 44. D232 | C2×C4 | semidirect |
| 78. #427 | D29 | semidirect |
| 96. #107 | C2×D29 | semidirect |
| 97. #106 | C2×D29 | semidirect |
| 101. C29 | #2948 | semidirect |
| 113. C2×C8 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D232 | 2 |
| #14271637 | 2 |
| #14271274 | 2 |
| #14271245 | 2 |
| #14271167 | 2 |
| #14271118 | 2 |
| C29×#427 | 2 |
| #2948 | 29 |