Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 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 |
|---|---|---|
| 3. #14271261 | C2 | semidirect |
| 4. C4×#90784 | C2 | semidirect |
| 5. #14271199 | C2 | semidirect |
| 6. #14271172 | C2 | semidirect |
| 8. #14271119 | C2 | semidirect |
| 9. C29×#519 | C2 | semidirect |
| 13. C4×Q8×C29 | C22 | semidirect |
| 17. C2×#90784 | C4 | semidirect |
| 26. #11745183 | C22 | semidirect |
| 28. #11745156 | C22 | semidirect |
| 29. #11745155 | C22 | semidirect |
| 30. #11745151 | C22 | semidirect |
| 31. C4×#6597 | C22 | semidirect |
| 35. C2×Q8×C29 | C2×C4 | semidirect |
| 53. #90784 | C2×C4 | semidirect |
| 54. #90784 | C2×C4 | semidirect |
| 59. C2×#6597 | C2×C4 | semidirect |
| 101. #519 | D29 | semidirect |
| 121. C4×Q8 | C2×D29 | semidirect |
| 135. C29 | #2949 | semidirect |
| 139. C2×Q8 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90784 | 2 |
| #14271637 | 2 |
| #14271261 | 2 |
| C4×#90784 | 2 |
| #14271199 | 2 |
| #14271172 | 2 |
| #14271167 | 2 |
| #14271119 | 2 |
| C29×#519 | 2 |
| #2949 | 29 |