Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
656 conjugacy classes of subgroups; only the 357 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 357 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. C4×#90772 | C2 | direct (N × H) |
| 4. C2×#11745163 | C2 | semidirect |
| 5. C2×C4×#6597 | C2 | semidirect |
| 6. C2×C4×C8×C29 | C2 | semidirect |
| 14. C2×#90772 | C4 | direct (N × H) |
| 18. C4×C8×C29 | C22 | semidirect |
| 19. #11745163 | C22 | semidirect |
| 20. C4×#6597 | C22 | semidirect |
| 31. C2×C8×C29 | C2×C4 | semidirect |
| 38. C2×#6597 | C2×C4 | semidirect |
| 40. #90772 | C2×C4 | direct (N × H) |
| 45. C2×C4×C29 | M16 | semidirect |
| 57. C8×C29 | C22×C4 | semidirect |
| 58. #6597 | C22×C4 | semidirect |
| 67. C4×C29 | C2×M16 | semidirect |
| 76. C2×C4×C8 | D29 | semidirect |
| 77. C2×C29 | C4×M16 | semidirect |
| 94. C4×C8 | C2×D29 | semidirect |
| 95. C29 | C2×C4×M16 | semidirect |
| 109. C2×C8 | C4×D29 | semidirect |
| 127. C2×C4 | #90772 | direct (N × H) |
| 133. C8 | C2×C4×D29 | semidirect |
| 143. C4 | C2×#90772 | direct (N × H) |
| 146. C2 | C4×#90772 | 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 |
| C4×#90772 | 2 |
| C2×#11745163 | 2 |
| C2×C4×#6597 | 2 |
| C2×C4×C8×C29 | 2 |
| C2×C4×M16 | 29 |