Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
732 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 165 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×#11745311 | C2 | semidirect |
| 2. C22×#90784 | C2 | semidirect |
| 3. #14271727 | C2 | semidirect |
| 4. #14271308 | C2 | semidirect |
| 5. #14271302 | C2 | semidirect |
| 6. #14271172 | C2 | semidirect |
| 7. #14271159 | C2 | semidirect |
| 8. #14271130 | C2 | semidirect |
| 9. C2×C29×2−1+4 | C2 | semidirect |
| 16. C2×#41×C29 | C22 | semidirect |
| 19. C22×Q8×C29 | C22 | semidirect |
| 33. #11745183 | C22 | semidirect |
| 34. #11745183 | C22 | semidirect |
| 35. #11745180 | C22 | semidirect |
| 36. C22⋊#6597 | C22 | semidirect |
| 45. #41×C29 | D4 | semidirect |
| 53. C2×Q8×C29 | D4 | semidirect |
| 140. C2×2−1+4 | D29 | semidirect |
| 161. C2×#41 | C2×D29 | semidirect |
| 164. C22×Q8 | C2×D29 | semidirect |
| 182. C29 | #3010 | semidirect |
| 191. #41 | C22⋊D29 | semidirect |
| 199. C2×Q8 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745311 | 2 |
| C22×#90784 | 2 |
| #14271727 | 2 |
| #14271308 | 2 |
| #14271302 | 2 |
| #14271172 | 2 |
| #14271159 | 2 |
| #14271130 | 2 |
| C2×C29×2−1+4 | 2 |
| #3010 | 29 |