Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
180 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 73 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. Q8×#6597 | C2 | semidirect |
| 4. #14270913 | C2 | semidirect |
| 6. C8×#6597 | C2 | semidirect |
| 7. C29×Q8⋊C8 | C2 | semidirect |
| 32. #90784 | C8 | semidirect |
| 43. Q8×C29 | C2×C8 | semidirect |
| 59. #6597 | C2×C8 | semidirect |
| 60. #6597 | SD16 | semidirect |
| 78. Q8⋊C8 | D29 | semidirect |
| 100. C29 | C8×SD16 | semidirect |
| 121. Q8 | C8×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#6597 | 2 |
| C4×#90784 | 2 |
| #14271228 | 2 |
| #14270913 | 2 |
| #14270892 | 2 |
| C8×#6597 | 2 |
| C29×Q8⋊C8 | 2 |
| C8×SD16 | 29 |