Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
780 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 325 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. #14271014 | C2 | semidirect |
| 3. C4×C22⋊Dic29 | C2 | semidirect |
| 4. #14271010 | C2 | semidirect |
| 5. #14271008 | C2 | semidirect |
| 6. #95×D29 | C2 | semidirect |
| 7. C2×C29×#95 | C2 | semidirect |
| 12. C4×C22⋊D29 | C4 | semidirect |
| 24. C22×C4×C29 | C2×C4 | semidirect |
| 32. C2×C4×D29 | C2×C4 | semidirect |
| 33. C22⋊Dic29 | C2×C4 | semidirect |
| 34. #90781 | C2×C4 | semidirect |
| 35. #90779 | C2×C4 | semidirect |
| 37. C4×Dic29 | C2×C4 | semidirect |
| 50. C22⋊D29 | C42 | semidirect |
| 79. C2×#95 | D29 | semidirect |
| 98. C29 | #2275 | semidirect |
| 108. 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×C4×C22⋊D29 | 2 |
| #14271014 | 2 |
| C4×C22⋊Dic29 | 2 |
| #14271010 | 2 |
| #14271008 | 2 |
| #95×D29 | 2 |
| C2×C29×#95 | 2 |
| #2275 | 29 |