Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
436 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 436 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. C2×#11745250 | C2 | semidirect |
| 3. #14271521 | C2 | direct (N × H) |
| 4. C2×#11745164 | C2 | semidirect |
| 5. C2×#11745158 | C2 | semidirect |
| 7. C2×#11745163 | C2 | semidirect |
| 23. #11745250 | C22 | semidirect |
| 26. #11745164 | C22 | semidirect |
| 27. #11745163 | C22 | semidirect |
| 28. #11745158 | C22 | semidirect |
| 113. C2×C29 | #489 | semidirect |
| 137. C29 | C2×#489 | semidirect |
| 213. C2 | #14271521 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745250 | 2 |
| C2×#11745298 | 2 |
| #14271521 | 2 |
| C2×#11745164 | 2 |
| C2×#11745158 | 2 |
| C2×#11745180 | 2 |
| C2×#11745163 | 2 |
| C2×C29×#102 | 2 |
| C2×#489 | 29 |