Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14271768 | C2 | semidirect |
| 2. #14271463 | C2 | semidirect |
| 3. #14271460 | C2 | semidirect |
| 4. #14271414 | C2 | semidirect |
| 5. #14271397 | C2 | semidirect |
| 6. #14271358 | C2 | semidirect |
| 7. #14271355 | C2 | semidirect |
| 8. #14271190 | C2 | semidirect |
| 9. C29×#540 | C2 | semidirect |
| 103. #540 | D29 | semidirect |
| 141. C29 | #3259 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271768 | 2 |
| #14271463 | 2 |
| #14271460 | 2 |
| #14271414 | 2 |
| #14271397 | 2 |
| #14271358 | 2 |
| #14271355 | 2 |
| #14271190 | 2 |
| C29×#540 | 2 |
| #3259 | 29 |