Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14271816 | C2 | semidirect |
| 2. D4×D116 | C2 | semidirect |
| 3. #14271511 | C2 | semidirect |
| 4. #14271478 | C2 | semidirect |
| 5. #14271400 | C2 | semidirect |
| 6. #14271359 | C2 | semidirect |
| 7. #14271298 | C2 | semidirect |
| 8. C4×#90782 | C2 | semidirect |
| 9. #14271228 | C2 | semidirect |
| 10. #102×D29 | C2 | semidirect |
| 11. C29×#474 | C2 | semidirect |
| 15. C29×C4⋊Q8 | C22 | semidirect |
| 20. C2×D232 | C22 | semidirect |
| 21. C2×C8×D29 | C22 | semidirect |
| 23. #11745257 | C22 | semidirect |
| 25. C4⋊C4×D29 | C22 | semidirect |
| 29. C4×D116 | C22 | semidirect |
| 30. C29×#107 | C22 | semidirect |
| 31. C29×C4⋊C8 | C22 | semidirect |
| 34. #11745169 | C22 | semidirect |
| 35. #11745168 | C22 | semidirect |
| 36. #11745157 | C22 | semidirect |
| 37. #11745157 | C22 | semidirect |
| 38. #11745157 | C22 | semidirect |
| 39. #11745155 | C22 | semidirect |
| 40. C4×#6597 | C22 | semidirect |
| 87. D4×C29 | #41 | semidirect |
| 105. D116 | D8 | semidirect |
| 140. #474 | D29 | semidirect |
| 160. C4⋊Q8 | C2×D29 | semidirect |
| 173. #107 | C2×D29 | semidirect |
| 174. C4⋊C8 | C2×D29 | semidirect |
| 183. C29 | #3294 | semidirect |
| 240. D4 | #90809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271816 | 2 |
| D4×D116 | 2 |
| #14271511 | 2 |
| #14271478 | 2 |
| #14271400 | 2 |
| #14271359 | 2 |
| #14271298 | 2 |
| C4×#90782 | 2 |
| #14271228 | 2 |
| #102×D29 | 2 |
| C29×#474 | 2 |
| #3294 | 29 |