Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
764 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#90807 | C2 | semidirect |
| 2. C2×#11745274 | C2 | semidirect |
| 3. #14271673 | C2 | semidirect |
| 4. #14271326 | C2 | semidirect |
| 5. #14271321 | C2 | semidirect |
| 6. #14271314 | C2 | semidirect |
| 7. #14271305 | C2 | semidirect |
| 8. #14271301 | C2 | semidirect |
| 9. #14271156 | C2 | semidirect |
| 10. C22⋊C8×D29 | C2 | semidirect |
| 11. C29×#447 | C2 | semidirect |
| 20. C2×#90807 | C22 | semidirect |
| 23. C2×D8×C29 | C22 | semidirect |
| 25. #11745300 | C22 | semidirect |
| 28. C2×#90783 | C22 | semidirect |
| 29. C2×#90783 | C22 | semidirect |
| 32. C2×Dic116 | C22 | semidirect |
| 33. C2×C8×D29 | C22 | semidirect |
| 34. #11745259 | C22 | semidirect |
| 35. #11745254 | C22 | semidirect |
| 38. C29×#102 | C22 | semidirect |
| 40. #11745180 | C22 | semidirect |
| 42. #11745168 | C22 | semidirect |
| 43. #11745164 | C22 | semidirect |
| 44. #11745158 | C22 | semidirect |
| 70. #90807 | D4 | semidirect |
| 151. C22×C29 | #135 | semidirect |
| 176. #447 | D29 | semidirect |
| 202. C2×D8 | C2×D29 | semidirect |
| 216. #102 | C2×D29 | semidirect |
| 220. C29 | #3002 | semidirect |
| 333. C22 | #11745274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90807 | 2 |
| C2×#11745274 | 2 |
| #14271673 | 2 |
| #14271326 | 2 |
| #14271321 | 2 |
| #14271314 | 2 |
| #14271305 | 2 |
| #14271301 | 2 |
| #14271156 | 2 |
| C22⋊C8×D29 | 2 |
| C29×#447 | 2 |
| #3002 | 29 |