Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
196 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 73 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. #14271228 | C2 | semidirect |
| 3. #14270890 | C2 | semidirect |
| 4. C8×#6597 | C2 | semidirect |
| 5. C29×#335 | C2 | semidirect |
| 27. D232 | C8 | semidirect |
| 35. D116 | C2×C8 | semidirect |
| 40. C8×C29 | C2×C8 | semidirect |
| 43. #6597 | D8 | semidirect |
| 57. #335 | D29 | semidirect |
| 74. C29 | C8×D8 | semidirect |
| 102. C8 | C8×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D232 | 2 |
| #14271228 | 2 |
| #14270890 | 2 |
| C8×#6597 | 2 |
| C29×#335 | 2 |
| C8×D8 | 29 |