Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 123 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. #14271818 | C2 | semidirect |
| 2. #14271798 | C2 | semidirect |
| 3. #14271509 | C2 | semidirect |
| 4. #14271475 | C2 | semidirect |
| 5. #14271444 | C2 | semidirect |
| 6. #14271396 | C2 | semidirect |
| 7. #14271295 | C2 | semidirect |
| 8. C4×#90782 | C2 | semidirect |
| 9. #14271228 | C2 | semidirect |
| 10. #102×D29 | C2 | semidirect |
| 11. C29×#459 | C2 | semidirect |
| 15. C2×D8×C29 | C22 | semidirect |
| 17. C4×D4×C29 | C22 | semidirect |
| 20. #11745300 | C22 | semidirect |
| 24. C2×C8×D29 | C22 | semidirect |
| 25. C4⋊C4×D29 | C22 | semidirect |
| 29. #11745231 | C22 | semidirect |
| 30. C29×C4⋊C8 | C22 | semidirect |
| 31. C29×#102 | C22 | semidirect |
| 32. #11745180 | C22 | semidirect |
| 33. #11745180 | C22 | semidirect |
| 34. #11745180 | C22 | semidirect |
| 36. #11745168 | C22 | semidirect |
| 37. #11745166 | C22 | semidirect |
| 39. #11745155 | C22 | semidirect |
| 40. C4×#6597 | C22 | semidirect |
| 103. D116 | D8 | semidirect |
| 104. D116 | #41 | semidirect |
| 142. #459 | D29 | semidirect |
| 158. C2×D8 | C2×D29 | semidirect |
| 170. C4×D4 | C2×D29 | semidirect |
| 174. C4⋊C8 | C2×D29 | semidirect |
| 180. #102 | C2×D29 | semidirect |
| 183. C29 | #3294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271818 | 2 |
| #14271798 | 2 |
| #14271509 | 2 |
| #14271475 | 2 |
| #14271444 | 2 |
| #14271396 | 2 |
| #14271295 | 2 |
| C4×#90782 | 2 |
| #14271228 | 2 |
| #102×D29 | 2 |
| C29×#459 | 2 |
| #3294 | 29 |