Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
456 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 3. #14271271 | C2 | semidirect |
| 4. #14271270 | C2 | semidirect |
| 5. #14271269 | C2 | semidirect |
| 6. C4×#90785 | C2 | semidirect |
| 7. #14271255 | C2 | semidirect |
| 11. C29×#441 | C2 | semidirect |
| 17. Q16×D29 | C4 | semidirect |
| 111. #441 | D29 | semidirect |
| 148. C29 | #2950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D29 | 2 |
| #14271639 | 2 |
| #14271271 | 2 |
| #14271270 | 2 |
| #14271269 | 2 |
| C4×#90785 | 2 |
| #14271255 | 2 |
| #14271198 | 2 |
| #14271170 | 2 |
| #14271120 | 2 |
| C29×#441 | 2 |
| #2950 | 29 |