Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 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 |
|---|---|---|
| 2. C2×#11745304 | C2 | semidirect |
| 3. #14271737 | C2 | semidirect |
| 4. #14271324 | C2 | semidirect |
| 5. #14271317 | C2 | semidirect |
| 6. #14271172 | C2 | semidirect |
| 7. #14271160 | C2 | semidirect |
| 8. #14271129 | C2 | semidirect |
| 9. C22×Q16×C29 | C2 | semidirect |
| 138. C22×Q16 | D29 | semidirect |
| 177. C29 | #3011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745362 | 2 |
| C2×#11745304 | 2 |
| #14271737 | 2 |
| #14271324 | 2 |
| #14271317 | 2 |
| #14271172 | 2 |
| #14271160 | 2 |
| #14271129 | 2 |
| C22×Q16×C29 | 2 |
| #3011 | 29 |