Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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. #14271718 | C2 | semidirect |
| 3. #14271500 | C2 | semidirect |
| 4. #14271440 | C2 | semidirect |
| 5. #14271369 | C2 | semidirect |
| 6. #14271368 | C2 | semidirect |
| 8. #14271262 | C2 | semidirect |
| 9. #14271260 | C2 | semidirect |
| 10. #14271219 | C2 | semidirect |
| 11. C29×#474 | C2 | semidirect |
| 14. C29×C4⋊Q8 | C22 | semidirect |
| 27. #11745249 | C22 | semidirect |
| 32. #11745231 | C22 | semidirect |
| 33. C29×#107 | C22 | semidirect |
| 34. C29×C4⋊C8 | C22 | semidirect |
| 37. #11745164 | C22 | semidirect |
| 38. #11745163 | C22 | semidirect |
| 39. #11745158 | C22 | semidirect |
| 41. #11745155 | C22 | semidirect |
| 42. C4⋊#6597 | C22 | semidirect |
| 145. #474 | D29 | semidirect |
| 163. C4⋊Q8 | C2×D29 | semidirect |
| 180. #107 | C2×D29 | semidirect |
| 182. C4⋊C8 | C2×D29 | semidirect |
| 189. C29 | #3110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271718 | 2 |
| C4×D4×D29 | 2 |
| #14271500 | 2 |
| #14271440 | 2 |
| #14271369 | 2 |
| #14271368 | 2 |
| #14271315 | 2 |
| #14271262 | 2 |
| #14271260 | 2 |
| #14271219 | 2 |
| C29×#474 | 2 |
| #3110 | 29 |