Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
384 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#11745252 | C2 | semidirect |
| 3. #14271473 | C2 | semidirect |
| 4. #14271469 | C2 | semidirect |
| 5. #14271466 | C2 | semidirect |
| 6. #14271462 | C2 | semidirect |
| 7. #14271206 | C2 | semidirect |
| 8. #14271186 | C2 | semidirect |
| 11. C29×#428 | C2 | semidirect |
| 138. #428 | D29 | semidirect |
| 178. C29 | #3080 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745252 | 2 |
| #14271631 | 2 |
| #14271473 | 2 |
| #14271469 | 2 |
| #14271466 | 2 |
| #14271462 | 2 |
| #14271206 | 2 |
| #14271186 | 2 |
| #14271165 | 2 |
| #14271162 | 2 |
| C29×#428 | 2 |
| #3080 | 29 |