Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
404 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 130 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 |
|---|---|---|
| 2. #14272031 | C2 | direct (N × H) |
| 8. #11745345 | C4 | semidirect |
| 11. C2×C4×#1181 | C4 | semidirect |
| 12. C22×C8×C29 | C4 | semidirect |
| 13. C22×#6597 | C4 | semidirect |
| 16. C2×#90772 | C4 | semidirect |
| 35. C4×#1181 | C2×C4 | semidirect |
| 38. C2×C8×C29 | C2×C4 | semidirect |
| 41. C2×#6597 | C2×C4 | semidirect |
| 95. C2×C29 | H(3,ℤ/4) | semidirect |
| 105. C22×C8 | #1181 | semidirect |
| 113. C29 | C2×H(3,ℤ/4) | semidirect |
| 133. C2×C8 | C2×#1181 | semidirect |
| 189. C2 | #14272031 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745345 | 2 |
| #14272031 | 2 |
| C22×#90772 | 2 |
| C2×H(3,ℤ/4) | 29 |