Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
284 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 77 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. #14270958 | C2 | direct (N × H) |
| 4. C22×Q8×C29 | C4 | semidirect |
| 7. C29×#124 | C4 | semidirect |
| 10. C2×C42×C29 | C4 | semidirect |
| 18. C2×Q8×C29 | C2×C4 | semidirect |
| 31. C42×C29 | C2×C4 | semidirect |
| 79. C2×C29 | #354 | semidirect |
| 81. C22×Q8 | Dic29 | semidirect |
| 84. #124 | Dic29 | semidirect |
| 88. C2×C42 | Dic29 | semidirect |
| 91. C29 | C2×#354 | semidirect |
| 96. C2×Q8 | C2×Dic29 | semidirect |
| 111. C42 | C2×Dic29 | semidirect |
| 153. C2 | #14270958 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745182 | 2 |
| #14270958 | 2 |
| C2×C29×#124 | 2 |
| C2×#354 | 29 |