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. #14272128 | C2 | direct (N × H) |
| 4. C2×#11745218 | C2 | semidirect |
| 5. C2×C4×#6599 | C2 | semidirect |
| 11. C2×#90796 | C4 | semidirect |
| 13. C2×D29⋊C8 | C4 | semidirect |
| 21. #11745218 | C22 | semidirect |
| 22. C4×#6599 | C22 | semidirect |
| 38. #90796 | C2×C4 | semidirect |
| 39. D29⋊C8 | C2×C4 | semidirect |
| 87. C2×C29 | #405 | semidirect |
| 108. C29 | C2×#405 | semidirect |
| 167. C2 | #14272128 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90796 | 2 |
| C22×D29⋊C8 | 2 |
| #14272128 | 2 |
| C2×#11745218 | 2 |
| C2×C4×#6599 | 2 |
| C2×#11745254 | 2 |
| C2×#405 | 29 |