Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
656 conjugacy classes of subgroups; only the 341 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 341 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. #14271115 | C2 | direct (N × H) |
| 4. C2×#11745151 | C2 | semidirect |
| 5. C2×C8×Dic29 | C2 | semidirect |
| 6. C2×C29×#97 | C2 | semidirect |
| 14. C2×#90772 | C4 | semidirect |
| 18. C29×#97 | C22 | semidirect |
| 19. C8×Dic29 | C22 | semidirect |
| 20. #11745151 | C22 | semidirect |
| 31. C2×C8×C29 | C2×C4 | semidirect |
| 38. C2×#6597 | C2×C4 | semidirect |
| 40. #90772 | C2×C4 | semidirect |
| 51. C2×Dic29 | M16 | semidirect |
| 57. C8×C29 | C22×C4 | semidirect |
| 58. #6597 | C22×C4 | semidirect |
| 70. Dic29 | C2×M16 | semidirect |
| 75. C2×#97 | D29 | semidirect |
| 77. C2×C29 | C4×M16 | semidirect |
| 93. #97 | C2×D29 | semidirect |
| 95. C29 | C2×C4×M16 | semidirect |
| 109. C2×C8 | C4×D29 | semidirect |
| 133. C8 | C2×C4×D29 | semidirect |
| 146. C2 | #14271115 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90772 | 2 |
| C2×C42×D29 | 2 |
| #14271115 | 2 |
| C2×#11745151 | 2 |
| C2×C8×Dic29 | 2 |
| C2×C29×#97 | 2 |
| C2×C4×M16 | 29 |