Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
448 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 1. #14271720 | C2 | semidirect |
| 3. #14271494 | C2 | semidirect |
| 4. #14271454 | C2 | semidirect |
| 5. #14271369 | C2 | semidirect |
| 7. C4×#90773 | C2 | semidirect |
| 8. C29×#431 | C2 | semidirect |
| 23. #11745231 | C22 | semidirect |
| 24. #11745231 | C22 | semidirect |
| 26. C4×Dic58 | C22 | semidirect |
| 27. C29×C4⋊C8 | C22 | semidirect |
| 29. C4×C8×C29 | C22 | semidirect |
| 31. #11745165 | C22 | semidirect |
| 32. #11745164 | C22 | semidirect |
| 71. C2×C4×C29 | SD16 | semidirect |
| 115. #431 | D29 | semidirect |
| 140. C4⋊C8 | C2×D29 | semidirect |
| 144. C4×C8 | C2×D29 | semidirect |
| 145. C29 | #3101 | semidirect |
| 195. C2×C4 | #90773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271720 | 2 |
| C2×C4×D116 | 2 |
| #14271494 | 2 |
| #14271454 | 2 |
| #14271369 | 2 |
| #14271316 | 2 |
| C4×#90773 | 2 |
| C29×#431 | 2 |
| #3101 | 29 |