Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14271794 | C2 | semidirect |
| 3. #14271530 | C2 | semidirect |
| 4. #14271524 | C2 | semidirect |
| 5. #14271519 | C2 | semidirect |
| 6. #14271512 | C2 | semidirect |
| 7. #14271172 | C2 | semidirect |
| 10. #14271118 | C2 | semidirect |
| 11. C2×C29×#103 | C2 | semidirect |
| 132. C2×#103 | D29 | semidirect |
| 168. C29 | #3137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271794 | 2 |
| #14271737 | 2 |
| #14271530 | 2 |
| #14271524 | 2 |
| #14271519 | 2 |
| #14271512 | 2 |
| #14271172 | 2 |
| #14271162 | 2 |
| #14271160 | 2 |
| #14271118 | 2 |
| C2×C29×#103 | 2 |
| #3137 | 29 |