Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
234 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 67 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. C4⋊C8×D29 | C2 | semidirect |
| 3. C4×#90772 | C2 | semidirect |
| 4. Q8⋊#6597 | C2 | semidirect |
| 5. #14270892 | C2 | semidirect |
| 6. #14270890 | C2 | semidirect |
| 7. C29×Q8⋊C8 | C2 | semidirect |
| 106. Q8⋊C8 | D29 | semidirect |
| 133. C29 | #1483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271700 | 2 |
| C4⋊C8×D29 | 2 |
| C4×#90772 | 2 |
| Q8⋊#6597 | 2 |
| #14270892 | 2 |
| #14270890 | 2 |
| C29×Q8⋊C8 | 2 |
| #1483 | 29 |