Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
704 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 2. C2×#11745304 | C2 | semidirect |
| 3. #14271737 | C2 | semidirect |
| 4. #14271344 | C2 | semidirect |
| 5. #14271339 | C2 | semidirect |
| 6. #14271180 | C2 | semidirect |
| 7. #14271179 | C2 | semidirect |
| 8. #14271145 | C2 | semidirect |
| 9. C2×C29×#137 | C2 | semidirect |
| 11. C22×Q8×C29 | C22 | semidirect |
| 25. C29×#137 | C22 | semidirect |
| 28. C2×M16×C29 | C22 | semidirect |
| 29. #11745309 | C22 | semidirect |
| 31. #11745306 | C22 | semidirect |
| 34. #11745304 | C22 | semidirect |
| 37. #11745288 | C22 | semidirect |
| 38. C2×#90777 | C22 | semidirect |
| 39. #11745185 | C22 | semidirect |
| 40. #11745173 | C22 | semidirect |
| 41. #11745172 | C22 | semidirect |
| 42. #11745171 | C22 | semidirect |
| 188. C2×#137 | D29 | semidirect |
| 215. C22×Q8 | C2×D29 | semidirect |
| 219. #137 | C2×D29 | semidirect |
| 225. C2×M16 | C2×D29 | semidirect |
| 235. C29 | #3022 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271999 | 2 |
| C2×#11745304 | 2 |
| #14271737 | 2 |
| #14271344 | 2 |
| #14271339 | 2 |
| #14271180 | 2 |
| #14271179 | 2 |
| #14271145 | 2 |
| C2×C29×#137 | 2 |
| #3022 | 29 |