Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
266 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 53 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×D8×D29 | C2 | semidirect |
| 2. C2×#11745174 | C2 | semidirect |
| 3. #14271396 | C2 | semidirect |
| 4. #14270965 | C2 | semidirect |
| 5. #14270964 | C2 | semidirect |
| 6. #14270942 | C2 | semidirect |
| 7. C2×C29×D16 | C2 | semidirect |
| 10. C2×D8×C29 | C22 | semidirect |
| 18. C2×C16×C29 | C22 | semidirect |
| 21. #11745166 | C22 | semidirect |
| 22. C2×#90768 | C22 | semidirect |
| 35. D8×C29 | D4 | semidirect |
| 42. D232 | D4 | semidirect |
| 84. C2×D29 | D16 | semidirect |
| 91. C2×D16 | D29 | semidirect |
| 109. C2×D8 | C2×D29 | semidirect |
| 115. C2×C16 | C2×D29 | semidirect |
| 118. C29 | #2184 | semidirect |
| 134. D8 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D29 | 2 |
| C2×#11745174 | 2 |
| #14271396 | 2 |
| #14270965 | 2 |
| #14270964 | 2 |
| #14270942 | 2 |
| C2×C29×D16 | 2 |
| #2184 | 29 |