Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
402 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 4. #14271070 | C2 | semidirect |
| 5. #14270925 | C2 | semidirect |
| 6. #14270917 | C2 | semidirect |
| 7. C2×C29×#103 | C2 | semidirect |
| 15. C2×#90784 | C4 | semidirect |
| 32. C2×Q8×C29 | C2×C4 | semidirect |
| 61. C2×#6597 | C2×C4 | semidirect |
| 94. C2×Dic29 | SD16 | semidirect |
| 128. C2×#103 | D29 | semidirect |
| 159. C29 | #1877 | semidirect |
| 166. C2×Q8 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90784 | 2 |
| C2×#11745255 | 2 |
| C2×#11745169 | 2 |
| #14271070 | 2 |
| #14270925 | 2 |
| #14270917 | 2 |
| C2×C29×#103 | 2 |
| #1877 | 29 |