Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
578 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 83 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. #14271636 | C2 | semidirect |
| 3. C2×#11745154 | C2 | semidirect |
| 4. #14271018 | C2 | semidirect |
| 5. #14271018 | C2 | semidirect |
| 6. #14270929 | C2 | semidirect |
| 7. C29×#342 | C2 | semidirect |
| 21. #11745244 | C4 | semidirect |
| 34. C23×D29 | C2×C4 | semidirect |
| 38. C22×C4×C29 | D4 | semidirect |
| 47. C22×Dic29 | D4 | semidirect |
| 56. C22⋊C4×C29 | C2×C4 | semidirect |
| 95. C22×D29 | C22⋊C4 | semidirect |
| 112. C2×Dic29 | C22⋊C4 | semidirect |
| 157. #342 | D29 | semidirect |
| 186. C29 | #1889 | semidirect |
| 211. C22×C4 | D116 | semidirect |
| 226. C22⋊C4 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745244 | 2 |
| #14271636 | 2 |
| C2×#11745154 | 2 |
| #14271018 | 2 |
| #14270929 | 2 |
| C29×#342 | 2 |
| #1889 | 29 |