Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
370 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 370 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. C2×#11745271 | C2 | semidirect |
| 2. C2×#11745313 | C2 | semidirect |
| 4. C2×#11745153 | C2 | semidirect |
| 5. #14271069 | C2 | semidirect |
| 6. #14270931 | C2 | semidirect |
| 7. C2×C29×#104 | C2 | semidirect |
| 57. C2×Dic58 | D4 | semidirect |
| 59. M16×C29 | D4 | semidirect |
| 71. #90777 | D4 | semidirect |
| 142. C2×#104 | D29 | semidirect |
| 175. C29 | #2007 | semidirect |
| 210. M16 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745271 | 2 |
| C2×#11745313 | 2 |
| #14271741 | 2 |
| C2×#11745153 | 2 |
| #14271069 | 2 |
| #14270931 | 2 |
| C2×C29×#104 | 2 |
| #2007 | 29 |