Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
370 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 75 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×#11745304 | C2 | semidirect |
| 3. C2×#11745185 | C2 | semidirect |
| 4. C2×#11745173 | C2 | semidirect |
| 5. #14271070 | C2 | semidirect |
| 6. #14270931 | C2 | semidirect |
| 7. C2×C29×#137 | C2 | semidirect |
| 41. C2×Q8×C29 | D4 | semidirect |
| 61. M16×C29 | D4 | semidirect |
| 73. #90777 | D4 | semidirect |
| 139. C2×#137 | D29 | semidirect |
| 175. C29 | #2007 | semidirect |
| 191. C2×Q8 | C22⋊D29 | 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×#11745304 | 2 |
| #14271741 | 2 |
| C2×#11745185 | 2 |
| C2×#11745173 | 2 |
| #14271070 | 2 |
| #14270931 | 2 |
| C2×C29×#137 | 2 |
| #2007 | 29 |