Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
390 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 123 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×Q8×Dic29 | C2 | semidirect |
| 3. #14271491 | C2 | semidirect |
| 5. #14271472 | C2 | semidirect |
| 6. #14271387 | C2 | semidirect |
| 8. Q16×Dic29 | C2 | semidirect |
| 9. #14271248 | C2 | semidirect |
| 10. #14271213 | C2 | semidirect |
| 11. C29×#451 | C2 | semidirect |
| 133. #451 | D29 | semidirect |
| 174. C29 | #3108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271699 | 2 |
| C2×Q8×Dic29 | 2 |
| #14271491 | 2 |
| #14271477 | 2 |
| #14271472 | 2 |
| #14271387 | 2 |
| #14271302 | 2 |
| Q16×Dic29 | 2 |
| #14271248 | 2 |
| #14271213 | 2 |
| C29×#451 | 2 |
| #3108 | 29 |