Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 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×#11745365 | C2 | semidirect |
| 2. C2×#11745271 | C2 | semidirect |
| 3. C2×#11745312 | C2 | semidirect |
| 4. #14271744 | C2 | semidirect |
| 5. #14271326 | C2 | semidirect |
| 6. #14271320 | C2 | semidirect |
| 7. #14271309 | C2 | semidirect |
| 8. #14271303 | C2 | semidirect |
| 9. C2×#11745158 | C2 | semidirect |
| 10. #14271131 | C2 | semidirect |
| 11. C29×#417 | C2 | semidirect |
| 46. #41×C29 | D4 | semidirect |
| 79. C2×Dic58 | D4 | semidirect |
| 171. #417 | D29 | semidirect |
| 214. C29 | #3013 | semidirect |
| 224. #41 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745365 | 2 |
| C2×#11745271 | 2 |
| C2×#11745312 | 2 |
| #14271744 | 2 |
| #14271326 | 2 |
| #14271320 | 2 |
| #14271309 | 2 |
| #14271303 | 2 |
| C2×#11745158 | 2 |
| #14271131 | 2 |
| C29×#417 | 2 |
| #3013 | 29 |