Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
332 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 89 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. #14271179 | C2 | semidirect |
| 3. #14271137 | C2 | semidirect |
| 4. #14270924 | C2 | semidirect |
| 5. C29×#568 | C2 | semidirect |
| 11. #11745309 | C4 | semidirect |
| 12. #11745306 | C4 | semidirect |
| 13. #11745302 | C4 | semidirect |
| 15. #11745298 | C4 | semidirect |
| 38. M16×C29 | D4 | semidirect |
| 91. #568 | D29 | semidirect |
| 116. C29 | #1884 | semidirect |
| 134. M16 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271709 | 2 |
| #14271179 | 2 |
| #14271137 | 2 |
| #14270924 | 2 |
| C29×#568 | 2 |
| #1884 | 29 |