Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
388 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×#11745151 | C2 | semidirect |
| 4. #14270925 | C2 | semidirect |
| 5. C4×C4⋊C4×C29 | C2 | semidirect |
| 15. C4×D116 | C4 | semidirect |
| 17. #11745157 | C4 | semidirect |
| 32. C4⋊C4×C29 | C2×C4 | semidirect |
| 41. C2×#6597 | C2×C4 | semidirect |
| 64. D116 | C42 | semidirect |
| 88. C4×C4⋊C4 | D29 | semidirect |
| 109. C29 | #1762 | semidirect |
| 128. C4⋊C4 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D116 | 2 |
| C2×#11745157 | 2 |
| C2×#11745151 | 2 |
| #14270925 | 2 |
| C4×C4⋊C4×C29 | 2 |
| #1762 | 29 |