Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
494 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 139 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. #14271817 | C2 | semidirect |
| 2. D4×D116 | C2 | semidirect |
| 3. #14271510 | C2 | semidirect |
| 4. #14271477 | C2 | semidirect |
| 5. #14271444 | C2 | semidirect |
| 6. #14271399 | C2 | semidirect |
| 7. #14271359 | C2 | semidirect |
| 8. #14271299 | C2 | semidirect |
| 9. C4×D232 | C2 | semidirect |
| 10. C2×#11745169 | C2 | semidirect |
| 11. C8×D4×C29 | C2 | semidirect |
| 15. C22×C8×C29 | C22 | semidirect |
| 18. #11745292 | C22 | semidirect |
| 19. C2×C4⋊Dic29 | C22 | semidirect |
| 21. C2×D232 | C22 | semidirect |
| 28. C4×D116 | C22 | semidirect |
| 29. #11745231 | C22 | semidirect |
| 30. C29×C4⋊C8 | C22 | semidirect |
| 31. C29×C22⋊C8 | C22 | semidirect |
| 32. C4×C8×C29 | C22 | semidirect |
| 35. #11745169 | C22 | semidirect |
| 36. #11745169 | C22 | semidirect |
| 37. #11745169 | C22 | semidirect |
| 38. #11745169 | C22 | semidirect |
| 39. #11745166 | C22 | semidirect |
| 40. #11745166 | C22 | semidirect |
| 85. D4×C29 | D8 | semidirect |
| 106. D116 | #41 | semidirect |
| 145. C8×D4 | D29 | semidirect |
| 159. C22×C8 | C2×D29 | semidirect |
| 174. C4⋊C8 | C2×D29 | semidirect |
| 181. C22⋊C8 | C2×D29 | semidirect |
| 182. C4×C8 | C2×D29 | semidirect |
| 183. C29 | #3294 | semidirect |
| 240. D4 | D232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271817 | 2 |
| D4×D116 | 2 |
| #14271510 | 2 |
| #14271477 | 2 |
| #14271444 | 2 |
| #14271399 | 2 |
| #14271359 | 2 |
| #14271299 | 2 |
| C4×D232 | 2 |
| C2×#11745169 | 2 |
| C8×D4×C29 | 2 |
| #3294 | 29 |