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. #14271818 | C2 | semidirect |
| 2. D4×D116 | C2 | semidirect |
| 3. #14271510 | C2 | semidirect |
| 4. #14271478 | C2 | semidirect |
| 5. #14271443 | C2 | semidirect |
| 6. #14271398 | C2 | semidirect |
| 7. #14271358 | C2 | semidirect |
| 8. #14271295 | C2 | semidirect |
| 9. C8×D116 | C2 | semidirect |
| 10. #102×D29 | C2 | semidirect |
| 11. C4×D8×C29 | C2 | semidirect |
| 17. C4×D4×C29 | C22 | semidirect |
| 18. #11745300 | C22 | semidirect |
| 19. C2×#90782 | C22 | semidirect |
| 22. C2×C8×D29 | C22 | semidirect |
| 24. C4⋊C4×D29 | C22 | semidirect |
| 29. #11745231 | C22 | semidirect |
| 30. C29×#107 | C22 | semidirect |
| 32. C29×#102 | C22 | semidirect |
| 33. C4×C8×C29 | C22 | semidirect |
| 35. #11745169 | C22 | semidirect |
| 36. #11745169 | C22 | semidirect |
| 37. #11745168 | C22 | semidirect |
| 38. #11745157 | C22 | semidirect |
| 39. #11745155 | C22 | semidirect |
| 40. C4⋊#6597 | C22 | semidirect |
| 88. D4×C29 | #41 | semidirect |
| 105. D116 | D8 | semidirect |
| 144. C4×D8 | D29 | semidirect |
| 170. C4×D4 | C2×D29 | semidirect |
| 173. #107 | C2×D29 | semidirect |
| 180. #102 | C2×D29 | semidirect |
| 182. C4×C8 | C2×D29 | semidirect |
| 183. C29 | #3294 | semidirect |
| 240. D4 | #90805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271818 | 2 |
| D4×D116 | 2 |
| #14271510 | 2 |
| #14271478 | 2 |
| #14271443 | 2 |
| #14271398 | 2 |
| #14271358 | 2 |
| #14271295 | 2 |
| C8×D116 | 2 |
| #102×D29 | 2 |
| C4×D8×C29 | 2 |
| #3294 | 29 |