Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
492 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 3. #14271204 | C2 | semidirect |
| 4. #14271202 | C2 | semidirect |
| 5. #14271201 | C2 | semidirect |
| 6. #14271199 | C2 | semidirect |
| 7. C29×#427 | C2 | semidirect |
| 13. C2×#90772 | C4 | semidirect |
| 22. C29×#107 | C22 | semidirect |
| 23. C29×#106 | C22 | semidirect |
| 24. #11745166 | C22 | semidirect |
| 25. #11745165 | C22 | semidirect |
| 26. #11745156 | C22 | semidirect |
| 27. #11745155 | C22 | semidirect |
| 36. C2×C8×C29 | C2×C4 | semidirect |
| 48. C2×#6597 | C2×C4 | semidirect |
| 50. #90772 | C2×C4 | semidirect |
| 51. #90772 | C2×C4 | semidirect |
| 90. #427 | D29 | semidirect |
| 111. #107 | C2×D29 | semidirect |
| 114. #106 | C2×D29 | semidirect |
| 115. C29 | #2911 | semidirect |
| 128. 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×#90772 | 2 |
| #117×D29 | 2 |
| #14271204 | 2 |
| #14271202 | 2 |
| #14271201 | 2 |
| #14271199 | 2 |
| C29×#427 | 2 |
| #2911 | 29 |