Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
596 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 177 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. #14271063 | C2 | semidirect |
| 3. #14271052 | C2 | semidirect |
| 4. #14271048 | C2 | semidirect |
| 5. #14271041 | C2 | semidirect |
| 6. #14271039 | C2 | semidirect |
| 7. C4×C22⋊Dic29 | C2 | semidirect |
| 8. #14271010 | C2 | semidirect |
| 9. C29×#381 | C2 | semidirect |
| 17. #11745292 | C4 | semidirect |
| 36. C22×C4×C29 | C2×C4 | semidirect |
| 43. C2×C22⋊D29 | C2×C4 | semidirect |
| 59. #90781 | C2×C4 | semidirect |
| 60. C4⋊Dic29 | C2×C4 | semidirect |
| 134. #381 | D29 | semidirect |
| 166. C29 | #2333 | semidirect |
| 183. C22×C4 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745292 | 2 |
| #14271063 | 2 |
| #14271052 | 2 |
| #14271048 | 2 |
| #14271041 | 2 |
| #14271039 | 2 |
| C4×C22⋊Dic29 | 2 |
| #14271010 | 2 |
| C29×#381 | 2 |
| #2333 | 29 |