Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
740 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 205 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. C2×C4×D116 | C2 | semidirect |
| 3. #14271066 | C2 | semidirect |
| 4. #14271064 | C2 | semidirect |
| 5. #14271042 | C2 | semidirect |
| 6. #14271039 | C2 | semidirect |
| 7. #14271028 | C2 | semidirect |
| 8. #14271009 | C2 | semidirect |
| 9. C2×C4×D4×C29 | C2 | semidirect |
| 20. #11745302 | C4 | semidirect |
| 34. C2×D4×C29 | C2×C4 | semidirect |
| 43. C2×C22⋊D29 | C2×C4 | semidirect |
| 49. C2×D116 | C2×C4 | semidirect |
| 54. C42×C29 | D4 | semidirect |
| 60. C4×Dic29 | C2×C4 | semidirect |
| 119. C2×C4×D4 | D29 | semidirect |
| 153. C29 | #2328 | semidirect |
| 164. C2×D4 | C4×D29 | semidirect |
| 184. C42 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745302 | 2 |
| C2×C4×D116 | 2 |
| #14271066 | 2 |
| #14271064 | 2 |
| #14271042 | 2 |
| #14271039 | 2 |
| #14271028 | 2 |
| #14271009 | 2 |
| C2×C4×D4×C29 | 2 |
| #2328 | 29 |