Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
390 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 85 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×M16×D29 | C2 | semidirect |
| 3. C2×#11745171 | C2 | semidirect |
| 4. C2×#11745171 | C2 | semidirect |
| 5. #14271126 | C2 | semidirect |
| 6. #14270932 | C2 | semidirect |
| 7. C29×#343 | C2 | semidirect |
| 54. M16×C29 | D4 | semidirect |
| 64. #90777 | D4 | semidirect |
| 129. C2×D29 | #100 | semidirect |
| 143. #343 | D29 | semidirect |
| 173. C29 | #1900 | semidirect |
| 204. M16 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D29 | 2 |
| C2×#11745257 | 2 |
| C2×#11745171 | 2 |
| #14271126 | 2 |
| #14270932 | 2 |
| C29×#343 | 2 |
| #1900 | 29 |