Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
512 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 309 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. #14271201 | C2 | direct (N × H) |
| 3. C2×#11745166 | C2 | semidirect |
| 4. C2×#11745165 | C2 | semidirect |
| 7. C22×C8×C29 | C4 | semidirect |
| 16. #11745166 | C22 | semidirect |
| 17. #11745165 | C22 | semidirect |
| 28. C2×C8×C29 | C2×C4 | semidirect |
| 70. C2×C29 | #427 | semidirect |
| 74. C22×C8 | Dic29 | semidirect |
| 85. C29 | C2×#427 | semidirect |
| 96. C2×C8 | C2×Dic29 | semidirect |
| 132. C2 | #14271201 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745288 | 2 |
| #14271201 | 2 |
| C2×#11745166 | 2 |
| C2×#11745165 | 2 |
| C23×C8×C29 | 2 |
| C2×#427 | 29 |