Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
572 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 288 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. #14272128 | C2 | semidirect |
| 3. C4×#90796 | C2 | semidirect |
| 4. C4×D29⋊C8 | C2 | semidirect |
| 7. #11745348 | C4 | direct (N × H) |
| 28. #90796 | C2×C4 | semidirect |
| 29. D29⋊C8 | C2×C4 | semidirect |
| 58. C4×C29 | #131 | semidirect |
| 60. Dic29 | #131 | semidirect |
| 85. C29 | C4×#131 | semidirect |
| 126. C4 | #11745348 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745348 | 2 |
| #14272128 | 2 |
| C4×#90796 | 2 |
| C4×D29⋊C8 | 2 |
| C4×#90809 | 2 |
| C4×#131 | 29 |