Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
406 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#11745231 | C2 | semidirect |
| 3. C2×#11745164 | C2 | semidirect |
| 5. C29×#336 | C2 | semidirect |
| 49. C2×C4×C29 | SD16 | semidirect |
| 86. #336 | D29 | semidirect |
| 105. C29 | #2013 | semidirect |
| 148. C2×C4 | #90773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90773 | 2 |
| C2×#11745231 | 2 |
| C2×#11745164 | 2 |
| #14271065 | 2 |
| C29×#336 | 2 |
| #2013 | 29 |