Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
210 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 61 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. #14270909 | C2 | semidirect |
| 5. Q8⋊#6597 | C2 | semidirect |
| 6. Q8⋊#6597 | C2 | semidirect |
| 7. C29×#557 | C2 | semidirect |
| 55. Q8×C29 | SD16 | semidirect |
| 87. #557 | D29 | semidirect |
| 115. C29 | #1626 | semidirect |
| 146. Q8 | #90784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271511 | 2 |
| #14271363 | 2 |
| #14270909 | 2 |
| Q8⋊#6597 | 2 |
| C29×#557 | 2 |
| #1626 | 29 |