Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#90784 | C2 | semidirect |
| 3. #14271637 | C2 | semidirect |
| 4. #14271375 | C2 | semidirect |
| 5. #14271365 | C2 | semidirect |
| 6. #14271190 | C2 | semidirect |
| 7. #14271172 | C2 | semidirect |
| 8. #14271159 | C2 | semidirect |
| 9. C29×#536 | C2 | semidirect |
| 13. C29×C4⋊Q8 | C22 | semidirect |
| 14. C29×#124 | C22 | semidirect |
| 29. #11745183 | C22 | semidirect |
| 30. #11745183 | C22 | semidirect |
| 31. #11745180 | C22 | semidirect |
| 32. C4⋊#6597 | C22 | semidirect |
| 114. #536 | D29 | semidirect |
| 136. C4⋊Q8 | C2×D29 | semidirect |
| 137. #124 | C2×D29 | semidirect |
| 149. C29 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745311 | 2 |
| C22×#90784 | 2 |
| #14271637 | 2 |
| #14271375 | 2 |
| #14271365 | 2 |
| #14271190 | 2 |
| #14271172 | 2 |
| #14271159 | 2 |
| C29×#536 | 2 |
| #3042 | 29 |