Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
176 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 51 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. #14271510 | C2 | semidirect |
| 2. #14271369 | C2 | semidirect |
| 4. #14271242 | C2 | semidirect |
| 5. #14270910 | C2 | semidirect |
| 6. #14270906 | C2 | semidirect |
| 7. C29×#334 | C2 | semidirect |
| 84. #334 | D29 | semidirect |
| 107. C29 | #1701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271510 | 2 |
| #14271369 | 2 |
| #14271359 | 2 |
| #14271242 | 2 |
| #14270910 | 2 |
| #14270906 | 2 |
| C29×#334 | 2 |
| #1701 | 29 |