Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 65 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. C2×#11745174 | C2 | semidirect |
| 2. #14271540 | C2 | semidirect |
| 3. C4×#90768 | C2 | semidirect |
| 4. C29×#493 | C2 | semidirect |
| 25. #90768 | D4 | semidirect |
| 44. C4×C29 | D16 | semidirect |
| 49. #493 | D29 | semidirect |
| 64. C29 | #2246 | semidirect |
| 94. C4 | #11745174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745174 | 2 |
| #14271540 | 2 |
| C4×#90768 | 2 |
| C29×#493 | 2 |
| #2246 | 29 |