Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
516 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 205 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. #14271047 | C2 | semidirect |
| 4. #14271031 | C2 | semidirect |
| 5. C4×#90779 | C2 | semidirect |
| 7. C43×C29 | C2 | semidirect |
| 17. #11745238 | C4 | direct (N × H) |
| 32. C42×C29 | C2×C4 | semidirect |
| 36. #90779 | C2×C4 | semidirect |
| 66. C4×C29 | #126 | semidirect |
| 76. C43 | D29 | semidirect |
| 95. C29 | C4×#126 | semidirect |
| 111. C42 | C4×D29 | semidirect |
| 142. C4 | #11745238 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745238 | 2 |
| #14271054 | 2 |
| #14271047 | 2 |
| #14271031 | 2 |
| C4×#90779 | 2 |
| C4×#90781 | 2 |
| C43×C29 | 2 |
| C4×#126 | 29 |