Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#90783 | C2 | semidirect |
| 2. #14271734 | C2 | semidirect |
| 3. #14271638 | C2 | semidirect |
| 4. #14271376 | C2 | semidirect |
| 5. #14271366 | C2 | semidirect |
| 6. #14271191 | C2 | semidirect |
| 7. #14271173 | C2 | semidirect |
| 8. #14271159 | C2 | semidirect |
| 18. #11745306 | C22 | semidirect |
| 19. #11745298 | C22 | semidirect |
| 29. #11745183 | C22 | semidirect |
| 30. #11745180 | C22 | semidirect |
| 31. #11745164 | C22 | semidirect |
| 32. #11745162 | C22 | semidirect |
| 149. C29 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90783 | 2 |
| #14271734 | 2 |
| #14271638 | 2 |
| #14271376 | 2 |
| #14271366 | 2 |
| #14271191 | 2 |
| #14271173 | 2 |
| #14271159 | 2 |
| C2×C29×AGL(1,ℤ/8) | 2 |
| #3042 | 29 |