Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
444 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 444 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. #14271715 | C2 | semidirect |
| 3. #14271499 | C2 | semidirect |
| 4. #14271496 | C2 | semidirect |
| 5. #14271441 | C2 | semidirect |
| 6. #14271366 | C2 | semidirect |
| 8. #14271264 | C2 | semidirect |
| 9. #14271260 | C2 | semidirect |
| 10. #14271217 | C2 | semidirect |
| 17. Q8×Dic29 | C22 | semidirect |
| 18. #11745306 | C22 | semidirect |
| 28. #11745250 | C22 | semidirect |
| 30. #11745249 | C22 | semidirect |
| 35. #11745183 | C22 | semidirect |
| 38. #11745166 | C22 | semidirect |
| 39. #11745164 | C22 | semidirect |
| 40. #11745163 | C22 | semidirect |
| 41. #11745162 | C22 | semidirect |
| 42. #11745155 | C22 | semidirect |
| 179. C29 | #3110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271715 | 2 |
| C2×D4×Dic29 | 2 |
| #14271499 | 2 |
| #14271496 | 2 |
| #14271441 | 2 |
| #14271366 | 2 |
| #14271314 | 2 |
| #14271264 | 2 |
| #14271260 | 2 |
| #14271217 | 2 |
| C29×#450 | 2 |
| #3110 | 29 |