Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
368 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 211 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. #14271581 | C2 | semidirect |
| 3. #14271580 | C2 | semidirect |
| 4. #14271579 | C2 | semidirect |
| 5. M32×D29 | C2 | semidirect |
| 6. C2×C16×D29 | C2 | semidirect |
| 7. C29×#504 | C2 | semidirect |
| 15. C29×M32 | C22 | semidirect |
| 16. C2×C16×C29 | C22 | semidirect |
| 17. #11745160 | C22 | semidirect |
| 18. C2×#90768 | C22 | semidirect |
| 19. #11745146 | C22 | semidirect |
| 22. C16×D29 | C22 | semidirect |
| 23. C16×D29 | C22 | semidirect |
| 73. #504 | D29 | direct (N × H) |
| 79. D29 | #504 | direct (N × H) |
| 89. M32 | C2×D29 | semidirect |
| 95. C2×C16 | C2×D29 | semidirect |
| 96. C29 | C2×#504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #131×D29 | 2 |
| #14271581 | 2 |
| #14271580 | 2 |
| #14271579 | 2 |
| M32×D29 | 2 |
| C2×C16×D29 | 2 |
| C29×#504 | 2 |
| C2×#504 | 29 |