Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
276 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 85 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. #14271215 | C2 | semidirect |
| 3. C4×C8×D29 | C2 | semidirect |
| 4. Q8⋊#6597 | C2 | semidirect |
| 5. #14270892 | C2 | semidirect |
| 6. #14270890 | C2 | semidirect |
| 7. C29×Q8⋊C8 | C2 | semidirect |
| 29. #90809 | C8 | semidirect |
| 60. Q8×C29 | C2×C8 | semidirect |
| 72. D116 | C2×C8 | semidirect |
| 109. Q8⋊C8 | D29 | semidirect |
| 136. C29 | #1476 | semidirect |
| 170. Q8 | C8×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#90809 | 2 |
| #14271215 | 2 |
| C4×C8×D29 | 2 |
| Q8⋊#6597 | 2 |
| #14270892 | 2 |
| #14270890 | 2 |
| C29×Q8⋊C8 | 2 |
| #1476 | 29 |