Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
350 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 129 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. #14271980 | C2 | semidirect |
| 2. #14271604 | C2 | semidirect |
| 3. #14271603 | C2 | semidirect |
| 4. #14271593 | C2 | semidirect |
| 5. C2×#11745177 | C2 | semidirect |
| 6. #14271580 | C2 | semidirect |
| 7. C29×#578 | C2 | semidirect |
| 71. #578 | D29 | semidirect |
| 97. C29 | #3417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271980 | 2 |
| #14271604 | 2 |
| #14271603 | 2 |
| #14271593 | 2 |
| C2×#11745177 | 2 |
| #14271580 | 2 |
| C29×#578 | 2 |
| #3417 | 29 |