Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
778 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 253 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. #14271646 | C2 | semidirect |
| 3. #14271169 | C2 | semidirect |
| 4. #14271165 | C2 | semidirect |
| 5. #14271160 | C2 | semidirect |
| 6. C2×#11745169 | C2 | semidirect |
| 7. C2×C29×#131 | C2 | semidirect |
| 10. #11745364 | C4 | semidirect |
| 16. C2×M16×C29 | C22 | semidirect |
| 17. C22×C8×C29 | C22 | semidirect |
| 20. #11745288 | C22 | semidirect |
| 21. C2×C4⋊Dic29 | C22 | semidirect |
| 22. #11745169 | C22 | semidirect |
| 23. #11745169 | C22 | semidirect |
| 24. #11745169 | C22 | semidirect |
| 25. #11745164 | C22 | semidirect |
| 26. #11745164 | C22 | semidirect |
| 38. #90805 | C2×C4 | semidirect |
| 41. C2×D116 | C2×C4 | semidirect |
| 94. C2×#131 | D29 | semidirect |
| 113. C2×M16 | C2×D29 | semidirect |
| 114. C22×C8 | C2×D29 | semidirect |
| 124. C29 | #2897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745364 | 2 |
| #14271646 | 2 |
| #14271169 | 2 |
| #14271165 | 2 |
| #14271160 | 2 |
| C2×#11745169 | 2 |
| C2×C29×#131 | 2 |
| #2897 | 29 |