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×#11745313 | C2 | semidirect |
| 2. C2×C4×Dic58 | C2 | semidirect |
| 3. #14271382 | C2 | semidirect |
| 4. #14271370 | C2 | semidirect |
| 5. #14271360 | C2 | semidirect |
| 6. #14271187 | C2 | semidirect |
| 7. #14271164 | C2 | semidirect |
| 49. C2×Dic58 | D4 | semidirect |
| 111. C4×C29 | #137 | semidirect |
| 154. C29 | #3037 | semidirect |
| 233. C4 | #11745313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745313 | 2 |
| C2×C4×Dic58 | 2 |
| #14271382 | 2 |
| #14271370 | 2 |
| #14271360 | 2 |
| #14271187 | 2 |
| #14271164 | 2 |
| C29×#532 | 2 |
| #3037 | 29 |