Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
224 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 121 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. #14270885 | C2 | semidirect |
| 5. C8×#6597 | C2 | semidirect |
| 6. C8×#6597 | C2 | semidirect |
| 7. C29×#322 | C2 | semidirect |
| 34. #90772 | C8 | semidirect |
| 48. C8×C29 | C2×C8 | semidirect |
| 50. #6597 | C2×C8 | semidirect |
| 51. #6597 | M16 | semidirect |
| 67. #322 | D29 | semidirect |
| 87. C29 | C8×M16 | semidirect |
| 118. C8 | C8×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271214 | 2 |
| C4×#90772 | 2 |
| C4×C8×D29 | 2 |
| #14270885 | 2 |
| C8×#6597 | 2 |
| C29×#322 | 2 |
| C8×M16 | 29 |