Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
592 conjugacy classes of subgroups; only the 298 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 298 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 |
|---|---|---|
| 3. #14272127 | C2 | direct (N × H) |
| 4. C2×#11745218 | C2 | semidirect |
| 5. C2×C4×#6599 | C2 | semidirect |
| 8. C2×#90800 | C4 | semidirect |
| 10. C22×#6599 | C4 | semidirect |
| 21. #11745218 | C22 | semidirect |
| 22. C4×#6599 | C22 | semidirect |
| 32. #90800 | C2×C4 | semidirect |
| 36. C2×#6599 | C2×C4 | semidirect |
| 85. C2×C29 | #405 | semidirect |
| 104. C29 | C2×#405 | semidirect |
| 160. C2 | #14272127 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90800 | 2 |
| C23×#6599 | 2 |
| #14272127 | 2 |
| C2×#11745218 | 2 |
| C2×C4×#6599 | 2 |
| C2×#11745239 | 2 |
| C2×#405 | 29 |