Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
484 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 145 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×#11745271 | C2 | semidirect |
| 3. C2×C4×Dic58 | C2 | semidirect |
| 4. #14271386 | C2 | semidirect |
| 5. #14271374 | C2 | semidirect |
| 6. #14271364 | C2 | semidirect |
| 7. #14271165 | C2 | semidirect |
| 8. C29×#423 | C2 | semidirect |
| 48. C2×Dic58 | D4 | semidirect |
| 110. C4×C29 | #137 | semidirect |
| 122. #423 | D29 | semidirect |
| 154. C29 | #3037 | semidirect |
| 233. C4 | #11745271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745271 | 2 |
| #14271713 | 2 |
| C2×C4×Dic58 | 2 |
| #14271386 | 2 |
| #14271374 | 2 |
| #14271364 | 2 |
| #14271165 | 2 |
| C29×#423 | 2 |
| #3037 | 29 |