Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
198 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 69 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. #14271568 | C2 | semidirect |
| 2. #14271561 | C2 | semidirect |
| 5. #14271514 | C2 | semidirect |
| 7. C29×#322 | C2 | semidirect |
| 54. C8×C29 | SD16 | semidirect |
| 72. #322 | D29 | semidirect |
| 90. C29 | #1714 | semidirect |
| 124. C8 | #90773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271568 | 2 |
| #14271561 | 2 |
| #14271536 | 2 |
| #14271514 | 2 |
| #14271510 | 2 |
| C29×#322 | 2 |
| #1714 | 29 |