Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 189 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. #14271276 | C2 | semidirect |
| 4. C4×D232 | C2 | semidirect |
| 5. #14271201 | C2 | semidirect |
| 6. #14271169 | C2 | semidirect |
| 7. C29×#405 | C2 | semidirect |
| 13. C2×D232 | C4 | semidirect |
| 18. C4×D116 | C22 | semidirect |
| 19. C29×#97 | C22 | semidirect |
| 20. C4×C8×C29 | C22 | semidirect |
| 21. #11745169 | C22 | semidirect |
| 22. #11745166 | C22 | semidirect |
| 23. #11745165 | C22 | semidirect |
| 28. C2×D116 | C2×C4 | semidirect |
| 32. C2×C8×C29 | C2×C4 | semidirect |
| 43. D232 | C2×C4 | semidirect |
| 44. D232 | C2×C4 | semidirect |
| 80. #405 | D29 | semidirect |
| 99. #97 | C2×D29 | semidirect |
| 100. C4×C8 | C2×D29 | semidirect |
| 101. C29 | #2948 | semidirect |
| 112. 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 |
| #14271276 | 2 |
| C4×D232 | 2 |
| #14271201 | 2 |
| #14271169 | 2 |
| C29×#405 | 2 |
| #2948 | 29 |