Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
448 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
| 2. #14271493 | C2 | semidirect |
| 3. #14271453 | C2 | semidirect |
| 4. #14271368 | C2 | semidirect |
| 6. C4×#90783 | C2 | semidirect |
| 7. #14271216 | C2 | semidirect |
| 23. #11745231 | C22 | semidirect |
| 24. #11745231 | C22 | semidirect |
| 26. C4×Dic58 | C22 | semidirect |
| 29. #11745158 | C22 | semidirect |
| 30. #11745156 | C22 | semidirect |
| 31. C4⋊#6597 | C22 | semidirect |
| 32. C4×#6597 | C22 | semidirect |
| 78. C2×C4×C29 | SD16 | semidirect |
| 145. C29 | #3101 | semidirect |
| 195. C2×C4 | #90783 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271720 | 2 |
| #14271493 | 2 |
| #14271453 | 2 |
| #14271368 | 2 |
| #14271314 | 2 |
| C4×#90783 | 2 |
| #14271216 | 2 |
| C2×C4×D4×C29 | 2 |
| #3101 | 29 |