Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
880 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 229 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×#11745234 | C2 | semidirect |
| 3. C2×C4⋊C4×D29 | C2 | semidirect |
| 4. #14271069 | C2 | semidirect |
| 5. #14271068 | C2 | semidirect |
| 6. #14271066 | C2 | semidirect |
| 7. #14271039 | C2 | semidirect |
| 8. #14271021 | C2 | semidirect |
| 9. C29×#390 | C2 | semidirect |
| 15. C2×#90807 | C4 | semidirect |
| 36. C2×D4×C29 | C2×C4 | semidirect |
| 45. C22×Dic29 | C2×C4 | semidirect |
| 58. C2×Dic58 | C2×C4 | semidirect |
| 102. C4×D29 | C22⋊C4 | semidirect |
| 133. #390 | D29 | semidirect |
| 165. C29 | #2311 | semidirect |
| 177. C2×D4 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90807 | 2 |
| C2×#11745234 | 2 |
| C2×C4⋊C4×D29 | 2 |
| #14271069 | 2 |
| #14271068 | 2 |
| #14271066 | 2 |
| #14271039 | 2 |
| #14271021 | 2 |
| C29×#390 | 2 |
| #2311 | 29 |