Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
440 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 149 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×D232 | C2 | semidirect |
| 2. C2×#11745174 | C2 | direct (N × H) |
| 3. C22×#90768 | C2 | semidirect |
| 4. C22×D8×C29 | C2 | semidirect |
| 8. C2×D8×C29 | C22 | semidirect |
| 11. C2×D232 | C22 | semidirect |
| 12. #11745174 | C22 | direct (N × H) |
| 13. C2×#90768 | C22 | semidirect |
| 22. D8×C29 | C23 | semidirect |
| 26. D232 | C23 | semidirect |
| 27. #90768 | C23 | semidirect |
| 44. C22×C29 | D16 | semidirect |
| 51. C22×D8 | D29 | semidirect |
| 55. C2×C29 | C2×D16 | semidirect |
| 63. C2×D8 | C2×D29 | semidirect |
| 67. C29 | C22×D16 | semidirect |
| 78. D8 | C22×D29 | semidirect |
| 99. C22 | #11745174 | direct (N × H) |
| 105. C2 | C2×#11745174 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D232 | 2 |
| C2×#11745174 | 2 |
| C22×#90768 | 2 |
| C22×D8×C29 | 2 |
| C22×D16 | 29 |