Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
756 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 198 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. #14272241 | C2 | semidirect |
| 2. #14272150 | C2 | semidirect |
| 3. #14272149 | C2 | semidirect |
| 4. D29⋊#100 | C2 | semidirect |
| 5. C2×#11745229 | C2 | semidirect |
| 19. C2×#90800 | C22 | semidirect |
| 21. D29⋊M16 | C22 | semidirect |
| 22. #11745229 | C22 | semidirect |
| 23. #11745229 | C22 | semidirect |
| 24. #11745221 | C22 | semidirect |
| 156. C29 | #2888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272241 | 2 |
| #14272150 | 2 |
| #14272149 | 2 |
| D29⋊#100 | 2 |
| C2×#11745229 | 2 |
| C2×#11745359 | 2 |
| #2888 | 29 |