Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
996 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 197 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. C22×#90783 | C2 | semidirect |
| 2. C2×#11745286 | C2 | semidirect |
| 3. #14271314 | C2 | direct (N × H) |
| 4. C2×#11745180 | C2 | semidirect |
| 5. C2×C22⋊#6597 | C2 | semidirect |
| 14. C22×Dic58 | C22 | semidirect |
| 17. C2×#90783 | C22 | semidirect |
| 18. C2×C4⋊Dic29 | C22 | semidirect |
| 20. #11745286 | C22 | semidirect |
| 22. C22×#6597 | C22 | semidirect |
| 23. #11745180 | C22 | semidirect |
| 24. C22⋊#6597 | C22 | semidirect |
| 48. C2×Dic58 | C23 | semidirect |
| 52. C4⋊Dic29 | C23 | semidirect |
| 55. C2×#6597 | C23 | semidirect |
| 66. C23×C29 | SD16 | semidirect |
| 98. C22×C29 | C2×SD16 | semidirect |
| 114. C2×C29 | #450 | semidirect |
| 136. C29 | C2×#450 | semidirect |
| 178. C23 | #90783 | semidirect |
| 209. C22 | C2×#90783 | semidirect |
| 219. C2 | #14271314 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90783 | 2 |
| C2×#11745286 | 2 |
| #14271314 | 2 |
| C2×#11745180 | 2 |
| C2×C22⋊#6597 | 2 |
| C23×D4×C29 | 2 |
| C2×#450 | 29 |