Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
176 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 71 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. #14271287 | C2 | semidirect |
| 4. #14270893 | C2 | semidirect |
| 6. #14270884 | C2 | semidirect |
| 7. C29×#335 | C2 | semidirect |
| 39. #90773 | C8 | semidirect |
| 53. Dic58 | C2×C8 | semidirect |
| 57. C8×C29 | C2×C8 | semidirect |
| 77. #335 | D29 | semidirect |
| 100. C29 | SD16⋊C8 | semidirect |
| 138. C8 | C8×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271287 | 2 |
| C4×#90773 | 2 |
| #14271228 | 2 |
| #14270893 | 2 |
| #14270890 | 2 |
| #14270884 | 2 |
| C29×#335 | 2 |
| SD16⋊C8 | 29 |