Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
648 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 173 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. #14271043 | C2 | semidirect |
| 3. #14271042 | C2 | semidirect |
| 4. #14271041 | C2 | semidirect |
| 5. #14271040 | C2 | semidirect |
| 6. #14271039 | C2 | semidirect |
| 7. #14271039 | C2 | semidirect |
| 8. #14271030 | C2 | semidirect |
| 9. C29×#386 | C2 | semidirect |
| 21. #11745302 | C4 | semidirect |
| 37. C2×D4×C29 | C2×C4 | semidirect |
| 47. C2×C22⋊D29 | C2×C4 | semidirect |
| 48. C2×C22⋊D29 | C2×C4 | semidirect |
| 56. C2×D116 | C2×C4 | semidirect |
| 67. C4×Dic29 | C2×C4 | semidirect |
| 147. #386 | D29 | semidirect |
| 179. C29 | #2380 | semidirect |
| 194. C2×D4 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745302 | 2 |
| #14271043 | 2 |
| #14271042 | 2 |
| #14271041 | 2 |
| #14271040 | 2 |
| #14271039 | 2 |
| #14271030 | 2 |
| C29×#386 | 2 |
| #2380 | 29 |