Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
338 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. Q8×Dic58 | C2 | semidirect |
| 4. #14271513 | C2 | semidirect |
| 6. #14271446 | C2 | semidirect |
| 8. #14271290 | C2 | semidirect |
| 9. #14271270 | C2 | semidirect |
| 11. C29×#462 | C2 | semidirect |
| 120. #462 | D29 | semidirect |
| 157. C29 | #3369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic58 | 2 |
| #14271887 | 2 |
| #14271524 | 2 |
| #14271513 | 2 |
| #14271454 | 2 |
| #14271446 | 2 |
| #14271387 | 2 |
| #14271290 | 2 |
| #14271270 | 2 |
| C4×#90784 | 2 |
| C29×#462 | 2 |
| #3369 | 29 |