Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
458 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 177 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. #14271929 | C2 | semidirect |
| 3. #14271284 | C2 | semidirect |
| 4. #14271279 | C2 | semidirect |
| 5. C2×#11745173 | C2 | semidirect |
| 6. M16×Dic29 | C2 | semidirect |
| 7. C29×#430 | C2 | semidirect |
| 13. #11745271 | C4 | semidirect |
| 14. #11745270 | C4 | semidirect |
| 15. #11745269 | C22 | semidirect |
| 19. C29×#108 | C22 | semidirect |
| 20. #11745173 | C22 | semidirect |
| 21. #11745173 | C22 | semidirect |
| 22. #11745163 | C22 | semidirect |
| 23. C8×Dic29 | C22 | semidirect |
| 44. Dic116 | C2×C4 | semidirect |
| 45. D232 | C2×C4 | semidirect |
| 46. #90773 | C2×C4 | semidirect |
| 86. #430 | D29 | semidirect |
| 104. #108 | C2×D29 | semidirect |
| 109. C29 | #2956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271963 | 2 |
| #14271929 | 2 |
| #14271284 | 2 |
| #14271279 | 2 |
| C2×#11745173 | 2 |
| M16×Dic29 | 2 |
| C29×#430 | 2 |
| #2956 | 29 |