Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1088 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 285 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. C2×#11745288 | C2 | semidirect |
| 3. #14271024 | C2 | semidirect |
| 4. #14271020 | C2 | semidirect |
| 6. C4×#90781 | C2 | semidirect |
| 7. C2×C29×#117 | C2 | semidirect |
| 13. C22×C4×D29 | C4 | semidirect |
| 17. C2×C4⋊C4×C29 | C22 | semidirect |
| 19. C2×C42×C29 | C22 | semidirect |
| 23. C2×C4⋊Dic29 | C22 | semidirect |
| 24. C2×C4×Dic29 | C22 | semidirect |
| 25. #11745179 | C22 | semidirect |
| 73. C2×C4×C29 | C22⋊C4 | semidirect |
| 102. C2×D29 | #117 | semidirect |
| 110. C2×#117 | D29 | semidirect |
| 132. C2×C4⋊C4 | C2×D29 | semidirect |
| 137. C2×C42 | C2×D29 | semidirect |
| 139. C29 | #2280 | semidirect |
| 195. C2×C4 | #90781 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D29 | 2 |
| C2×#11745288 | 2 |
| #14271024 | 2 |
| #14271020 | 2 |
| #14271018 | 2 |
| C4×#90781 | 2 |
| C2×C29×#117 | 2 |
| #2280 | 29 |