Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
432 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 3. #14270932 | C2 | semidirect |
| 4. #14270931 | C2 | semidirect |
| 5. C29×#343 | C2 | semidirect |
| 14. M16×D29 | C4 | semidirect |
| 33. M16×C29 | C2×C4 | semidirect |
| 39. #90777 | C2×C4 | semidirect |
| 92. #343 | D29 | direct (N × H) |
| 99. D29 | #343 | direct (N × H) |
| 113. C29 | C2×#343 | semidirect |
| 131. M16 | C4×D29 | 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×C4⋊C4×D29 | 2 |
| #14270932 | 2 |
| #14270931 | 2 |
| C29×#343 | 2 |
| C2×#343 | 29 |