Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
270 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 1. #14271137 | C2 | semidirect |
| 2. #14270956 | C2 | semidirect |
| 5. C22×D4×C29 | C4 | semidirect |
| 7. C29×#124 | C4 | semidirect |
| 10. C29×#117 | C4 | semidirect |
| 13. #11745182 | C22 | semidirect |
| 74. C22×D4 | Dic29 | semidirect |
| 76. #124 | Dic29 | semidirect |
| 80. #117 | Dic29 | semidirect |
| 83. C29 | #2128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271137 | 2 |
| #14270956 | 2 |
| C29×#535 | 2 |
| #2128 | 29 |