Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
224 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 69 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. #14271537 | C2 | semidirect |
| 3. #14271511 | C2 | semidirect |
| 4. C8×#6597 | C2 | semidirect |
| 5. C29×#500 | C2 | semidirect |
| 36. C8×C29 | SD16 | semidirect |
| 38. #6597 | D8 | semidirect |
| 48. #500 | D29 | semidirect |
| 66. C29 | #1706 | semidirect |
| 90. C8 | #90784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271540 | 2 |
| #14271537 | 2 |
| #14271511 | 2 |
| C8×#6597 | 2 |
| C29×#500 | 2 |
| #1706 | 29 |