Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 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. #14271886 | C2 | semidirect |
| 2. #14271509 | C2 | semidirect |
| 4. #14270908 | C2 | semidirect |
| 5. Q8⋊#6597 | C2 | semidirect |
| 6. #14270890 | C2 | semidirect |
| 7. C29×#460 | C2 | semidirect |
| 93. #460 | D29 | semidirect |
| 120. C29 | #1628 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271886 | 2 |
| #14271509 | 2 |
| #14271355 | 2 |
| #14270908 | 2 |
| Q8⋊#6597 | 2 |
| #14270890 | 2 |
| C29×#460 | 2 |
| #1628 | 29 |