Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
458 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 185 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. #14271286 | C2 | semidirect |
| 4. #14271281 | C2 | semidirect |
| 5. #14271212 | C2 | semidirect |
| 6. C2×#11745153 | C2 | semidirect |
| 7. C4×M16×C29 | C2 | semidirect |
| 13. #11745271 | C4 | semidirect |
| 14. #11745270 | C4 | semidirect |
| 18. #11745263 | C22 | semidirect |
| 19. C29×#97 | C22 | semidirect |
| 20. C4×C8×C29 | C22 | semidirect |
| 21. #11745167 | C22 | semidirect |
| 22. #11745153 | C22 | semidirect |
| 23. #11745153 | C22 | semidirect |
| 44. Dic116 | C2×C4 | semidirect |
| 45. D232 | C2×C4 | semidirect |
| 46. #90773 | C2×C4 | semidirect |
| 88. C4×M16 | D29 | semidirect |
| 107. #97 | C2×D29 | semidirect |
| 108. C4×C8 | 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 |
| #14271286 | 2 |
| #14271281 | 2 |
| #14271212 | 2 |
| C2×#11745153 | 2 |
| C4×M16×C29 | 2 |
| #2956 | 29 |