Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
362 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 362 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. #14271181 | C2 | semidirect |
| 3. C2×#11745181 | C2 | semidirect |
| 4. #14270919 | C2 | semidirect |
| 5. C29×#518 | C2 | semidirect |
| 12. #11745302 | C4 | semidirect |
| 14. #11745298 | C4 | semidirect |
| 30. C2×D116 | C2×C4 | semidirect |
| 32. C2×Dic58 | C2×C4 | semidirect |
| 36. C42×C29 | D4 | semidirect |
| 40. C4×Dic29 | C2×C4 | semidirect |
| 84. #518 | D29 | semidirect |
| 107. C29 | #1911 | semidirect |
| 132. C42 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271730 | 2 |
| #14271181 | 2 |
| C2×#11745181 | 2 |
| #14270919 | 2 |
| C29×#518 | 2 |
| #1911 | 29 |