Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
488 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11745311 | C2 | semidirect |
| 2. C22×D232 | C2 | semidirect |
| 3. #14271433 | C2 | direct (N × H) |
| 4. C2×#11745167 | C2 | semidirect |
| 5. C2×#11745171 | C2 | semidirect |
| 6. C2×C29×#131 | C2 | semidirect |
| 10. C29×#131 | C22 | semidirect |
| 16. #11745311 | C22 | semidirect |
| 23. C2×D232 | C22 | semidirect |
| 24. #11745171 | C22 | semidirect |
| 25. #11745167 | C22 | semidirect |
| 105. C2×#131 | D29 | semidirect |
| 112. C2×C29 | #472 | semidirect |
| 126. #131 | C2×D29 | semidirect |
| 134. C29 | C2×#472 | semidirect |
| 215. C2 | #14271433 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745311 | 2 |
| C22×D232 | 2 |
| #14271433 | 2 |
| C2×#11745167 | 2 |
| C2×#11745171 | 2 |
| C2×C29×#131 | 2 |
| C2×#472 | 29 |