Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 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×#11745311 | C2 | semidirect |
| 3. C22×#90773 | C2 | semidirect |
| 4. #14271732 | C2 | semidirect |
| 5. #14271309 | C2 | semidirect |
| 6. #14271303 | C2 | semidirect |
| 7. #14271171 | C2 | semidirect |
| 8. #14271129 | C2 | semidirect |
| 9. C29×#416 | C2 | semidirect |
| 13. C2×Q8×D29 | C22 | semidirect |
| 15. C2×#90807 | C22 | semidirect |
| 33. C29×#103 | C22 | semidirect |
| 34. C29×#102 | C22 | semidirect |
| 35. #11745168 | C22 | semidirect |
| 36. #11745158 | C22 | semidirect |
| 39. #41×C29 | D4 | semidirect |
| 70. C2×Dic58 | D4 | semidirect |
| 147. #416 | D29 | semidirect |
| 179. #103 | C2×D29 | semidirect |
| 180. #102 | C2×D29 | semidirect |
| 182. C29 | #3010 | semidirect |
| 191. #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×#11745311 | 2 |
| C22×#90773 | 2 |
| #14271732 | 2 |
| #14271309 | 2 |
| #14271303 | 2 |
| #14271171 | 2 |
| #14271129 | 2 |
| C29×#416 | 2 |
| #3010 | 29 |