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. C22×#90783 | C2 | semidirect |
| 3. #14271730 | C2 | semidirect |
| 4. #14271305 | C2 | semidirect |
| 5. #14271300 | C2 | semidirect |
| 6. #14271173 | C2 | semidirect |
| 7. #14271159 | C2 | semidirect |
| 8. #14271131 | C2 | semidirect |
| 9. C2×C29×AGL(1,ℤ/8) | C2 | semidirect |
| 14. C2×Q8×D29 | C22 | semidirect |
| 16. C2×#90807 | C22 | semidirect |
| 33. #11745183 | C22 | semidirect |
| 34. #11745180 | C22 | semidirect |
| 35. #11745168 | C22 | semidirect |
| 36. #11745164 | C22 | semidirect |
| 39. #41×C29 | D4 | semidirect |
| 70. C2×Dic58 | D4 | semidirect |
| 141. C2×AGL(1,ℤ/8) | D29 | semidirect |
| 182. C29 | #3010 | semidirect |
| 191. #41 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745365 | 2 |
| C22×#90783 | 2 |
| #14271730 | 2 |
| #14271305 | 2 |
| #14271300 | 2 |
| #14271173 | 2 |
| #14271159 | 2 |
| #14271131 | 2 |
| C2×C29×AGL(1,ℤ/8) | 2 |
| #3010 | 29 |