Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
460 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 202 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. #14272178 | C2 | direct (N × H) |
| 4. C2×#11745212 | C2 | semidirect |
| 5. C2×#11745211 | C2 | semidirect |
| 25. #11745212 | C22 | semidirect |
| 26. #11745211 | C22 | semidirect |
| 111. C2×C29 | #430 | semidirect |
| 136. C29 | C2×#430 | semidirect |
| 217. C2 | #14272178 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90796 | 2 |
| C2×D29⋊M16 | 2 |
| #14272178 | 2 |
| C2×#11745212 | 2 |
| C2×#11745211 | 2 |
| C2×M16×D29 | 2 |
| C2×#430 | 29 |