Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
384 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 3. C2×C4×#6597 | C2 | semidirect |
| 4. C2×C8×Dic29 | C2 | semidirect |
| 6. #14270917 | C2 | semidirect |
| 7. C29×#336 | C2 | semidirect |
| 18. C2×C8×D29 | C4 | semidirect |
| 20. #11745168 | C4 | semidirect |
| 42. #90781 | C8 | semidirect |
| 60. C2×C4×C29 | C2×C8 | semidirect |
| 72. C2×Dic29 | C2×C8 | semidirect |
| 80. #6597 | C22⋊C4 | semidirect |
| 91. C2×D29 | C4×C8 | semidirect |
| 105. #336 | D29 | semidirect |
| 127. C29 | C8×C22⋊C4 | semidirect |
| 175. C2×C4 | C8×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D29 | 2 |
| C2×#11745168 | 2 |
| C2×C4×#6597 | 2 |
| C2×C8×Dic29 | 2 |
| C4×#90781 | 2 |
| #14270917 | 2 |
| C29×#336 | 2 |
| C8×C22⋊C4 | 29 |