Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
286 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 83 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. #14271205 | C2 | semidirect |
| 5. #14271028 | C2 | semidirect |
| 6. #14270924 | C2 | semidirect |
| 7. C29×#343 | C2 | semidirect |
| 21. #11745173 | C4 | semidirect |
| 42. M16×C29 | C2×C4 | semidirect |
| 57. C4×Dic29 | C2×C4 | semidirect |
| 111. #343 | D29 | semidirect |
| 137. C29 | #1860 | semidirect |
| 154. M16 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271644 | 2 |
| #14271205 | 2 |
| C2×#11745173 | 2 |
| #14271165 | 2 |
| #14271028 | 2 |
| #14270924 | 2 |
| C29×#343 | 2 |
| #1860 | 29 |