Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
188 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 53 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. #14271537 | C2 | semidirect |
| 2. #14271440 | C2 | semidirect |
| 4. #14271228 | C2 | semidirect |
| 5. #14270913 | C2 | semidirect |
| 6. #14270906 | C2 | semidirect |
| 7. C29×#332 | C2 | semidirect |
| 58. D116 | SD16 | semidirect |
| 65. #6597 | D8 | semidirect |
| 86. #332 | D29 | semidirect |
| 108. C29 | #1665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271537 | 2 |
| #14271440 | 2 |
| #14271359 | 2 |
| #14271228 | 2 |
| #14270913 | 2 |
| #14270906 | 2 |
| C29×#332 | 2 |
| #1665 | 29 |