Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
512 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 512 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 |
|---|---|---|
| 3. #14271060 | C2 | semidirect |
| 4. #14271057 | C2 | semidirect |
| 5. #14271051 | C2 | semidirect |
| 6. #14271045 | C2 | semidirect |
| 7. #14271036 | C2 | semidirect |
| 8. #14271021 | C2 | semidirect |
| 19. #11745297 | C4 | semidirect |
| 44. C22×Dic29 | C2×C4 | semidirect |
| 54. C22⋊Dic29 | C2×C4 | semidirect |
| 59. #90779 | C2×C4 | semidirect |
| 158. C29 | #2376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745297 | 2 |
| #14271066 | 2 |
| #14271060 | 2 |
| #14271057 | 2 |
| #14271051 | 2 |
| #14271045 | 2 |
| #14271036 | 2 |
| #14271021 | 2 |
| C29×#386 | 2 |
| #2376 | 29 |