Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 123 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. #14271818 | C2 | semidirect |
| 2. #14271515 | C2 | semidirect |
| 3. #14271504 | C2 | semidirect |
| 4. #14271450 | C2 | semidirect |
| 5. #14271390 | C2 | semidirect |
| 6. #14271368 | C2 | semidirect |
| 7. #14271306 | C2 | semidirect |
| 8. C4×#90782 | C2 | semidirect |
| 9. D4×#6597 | C2 | semidirect |
| 10. #14271157 | C2 | semidirect |
| 11. C29×#555 | C2 | semidirect |
| 125. #555 | D29 | semidirect |
| 171. C29 | #3303 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271818 | 2 |
| #14271515 | 2 |
| #14271504 | 2 |
| #14271450 | 2 |
| #14271390 | 2 |
| #14271368 | 2 |
| #14271306 | 2 |
| C4×#90782 | 2 |
| D4×#6597 | 2 |
| #14271157 | 2 |
| C29×#555 | 2 |
| #3303 | 29 |