Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
492 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 129 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. #14271708 | C2 | semidirect |
| 2. C2×D4×Dic29 | C2 | semidirect |
| 3. #14271477 | C2 | semidirect |
| 4. #14271474 | C2 | semidirect |
| 5. #14271441 | C2 | semidirect |
| 6. #14271356 | C2 | semidirect |
| 7. #14271297 | C2 | semidirect |
| 8. D8×Dic29 | C2 | semidirect |
| 9. #14271243 | C2 | semidirect |
| 10. #14271213 | C2 | semidirect |
| 11. C29×#447 | C2 | semidirect |
| 18. #11745302 | C22 | semidirect |
| 24. D4×Dic29 | C22 | semidirect |
| 29. #11745255 | C22 | semidirect |
| 30. #11745250 | C22 | semidirect |
| 36. #11745180 | C22 | semidirect |
| 38. #11745169 | C22 | semidirect |
| 39. #11745166 | C22 | semidirect |
| 40. #11745162 | C22 | semidirect |
| 41. C8×Dic29 | C22 | semidirect |
| 42. #11745155 | C22 | semidirect |
| 94. D4×C29 | #41 | semidirect |
| 109. C2×Dic29 | D8 | semidirect |
| 150. #447 | D29 | semidirect |
| 192. C29 | #3100 | semidirect |
| 249. D4 | #90807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271708 | 2 |
| C2×D4×Dic29 | 2 |
| #14271477 | 2 |
| #14271474 | 2 |
| #14271441 | 2 |
| #14271356 | 2 |
| #14271297 | 2 |
| D8×Dic29 | 2 |
| #14271243 | 2 |
| #14271213 | 2 |
| C29×#447 | 2 |
| #3100 | 29 |