Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
754 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 169 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. C2×#11745313 | C2 | semidirect |
| 2. C2×#11745286 | C2 | semidirect |
| 3. #14271325 | C2 | semidirect |
| 4. #14271319 | C2 | semidirect |
| 5. #14271314 | C2 | semidirect |
| 6. #14271164 | C2 | semidirect |
| 7. #14271127 | C2 | semidirect |
| 19. C22×Dic58 | C22 | semidirect |
| 22. C2×#90785 | C22 | semidirect |
| 23. C2×#90783 | C22 | semidirect |
| 24. C2×C4⋊Dic29 | C22 | semidirect |
| 28. #11745286 | C22 | semidirect |
| 30. C2×#90777 | C22 | semidirect |
| 31. #11745183 | C22 | semidirect |
| 32. #11745180 | C22 | semidirect |
| 34. C22⋊#6597 | C22 | semidirect |
| 131. C22×C29 | #137 | semidirect |
| 181. C29 | #3007 | semidirect |
| 276. C22 | #11745313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745313 | 2 |
| C2×#11745286 | 2 |
| #14271325 | 2 |
| #14271319 | 2 |
| #14271314 | 2 |
| #14271164 | 2 |
| #14271127 | 2 |
| C22×#41×C29 | 2 |
| #3007 | 29 |