Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
452 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 137 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. #14271963 | C2 | semidirect |
| 2. C2×#11745266 | C2 | semidirect |
| 3. C2×#11745263 | C2 | semidirect |
| 4. #14271439 | C2 | semidirect |
| 5. #14271434 | C2 | semidirect |
| 6. #14271427 | C2 | semidirect |
| 7. #14271145 | C2 | semidirect |
| 8. C2×C29×#108 | C2 | semidirect |
| 18. C2×Dic116 | C22 | semidirect |
| 24. C2×D232 | C22 | semidirect |
| 25. C2×#90773 | C22 | semidirect |
| 32. C29×#108 | C22 | semidirect |
| 33. C29×#108 | C22 | semidirect |
| 34. #11745172 | C22 | semidirect |
| 35. #11745171 | C22 | semidirect |
| 133. C2×#108 | D29 | semidirect |
| 164. #108 | C2×D29 | semidirect |
| 165. #108 | C2×D29 | semidirect |
| 168. C29 | #3067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271963 | 2 |
| C2×#11745266 | 2 |
| C2×#11745263 | 2 |
| #14271439 | 2 |
| #14271434 | 2 |
| #14271427 | 2 |
| #14271145 | 2 |
| C2×C29×#108 | 2 |
| #3067 | 29 |