Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11745231 | C2 | semidirect |
| 3. #14271459 | C2 | semidirect |
| 4. #14271454 | C2 | semidirect |
| 5. #14271449 | C2 | semidirect |
| 6. #14271444 | C2 | semidirect |
| 7. #14271205 | C2 | semidirect |
| 9. C29×#423 | C2 | semidirect |
| 41. #90805 | Q8 | semidirect |
| 89. D116 | C2×Q8 | semidirect |
| 96. Dic58 | C2×Q8 | semidirect |
| 124. #423 | D29 | semidirect |
| 156. C29 | #3079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745231 | 2 |
| C4×#90805 | 2 |
| #14271459 | 2 |
| #14271454 | 2 |
| #14271449 | 2 |
| #14271444 | 2 |
| #14271205 | 2 |
| #14271165 | 2 |
| C29×#423 | 2 |
| #3079 | 29 |