Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
160 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 160 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. #14271567 | C2 | semidirect |
| 3. #14270965 | C2 | semidirect |
| 4. #14270964 | C2 | semidirect |
| 5. #14270963 | C2 | semidirect |
| 6. C16×Dic29 | C2 | semidirect |
| 7. C29×#357 | C2 | semidirect |
| 73. #357 | D29 | semidirect |
| 91. C29 | #2240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271567 | 2 |
| #14271538 | 2 |
| #14270965 | 2 |
| #14270964 | 2 |
| #14270963 | 2 |
| C16×Dic29 | 2 |
| C29×#357 | 2 |
| #2240 | 29 |