Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1224 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 277 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×C4×C22⋊D29 | C2 | semidirect |
| 3. #14271042 | C2 | semidirect |
| 4. #14271036 | C2 | semidirect |
| 5. #14271019 | C2 | semidirect |
| 6. C4×C22⋊Dic29 | C2 | semidirect |
| 7. C24×C4×C29 | C2 | semidirect |
| 13. C22×C4×D29 | C22 | semidirect |
| 14. #11745315 | C4 | direct (N × H) |
| 19. C2×#90781 | C22 | semidirect |
| 20. C2×#90779 | C22 | semidirect |
| 21. C2×C4×Dic29 | C22 | semidirect |
| 22. #11745179 | C22 | semidirect |
| 25. C24×C29 | C2×C4 | semidirect |
| 32. C22×C4×C29 | D4 | semidirect |
| 37. C2×C22⋊D29 | C2×C4 | semidirect |
| 44. C22⋊Dic29 | C2×C4 | semidirect |
| 59. C22×D29 | C22×C4 | semidirect |
| 71. C2×Dic29 | C22×C4 | semidirect |
| 79. C22×C29 | C4×D4 | semidirect |
| 87. C4×C29 | #120 | semidirect |
| 91. C24×C4 | D29 | semidirect |
| 118. C29 | C4×#120 | semidirect |
| 122. C24 | C4×D29 | semidirect |
| 135. C22×C4 | C22⋊D29 | semidirect |
| 177. C22 | C4×C22⋊D29 | semidirect |
| 185. C4 | #11745315 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745315 | 2 |
| C2×C4×C22⋊D29 | 2 |
| #14271042 | 2 |
| #14271036 | 2 |
| #14271019 | 2 |
| C4×C22⋊Dic29 | 2 |
| C24×C4×C29 | 2 |
| C4×#120 | 29 |