Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
126 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 45 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. #14271560 | C2 | semidirect |
| 3. #14270986 | C2 | semidirect |
| 4. #14270985 | C2 | semidirect |
| 5. #14270983 | C2 | semidirect |
| 21. Q16×C29 | Q8 | semidirect |
| 23. D8×C29 | Q8 | semidirect |
| 79. C29 | #2230 | semidirect |
| 82. Q16 | Dic58 | semidirect |
| 84. D8 | Dic58 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271560 | 2 |
| #14271280 | 2 |
| #14270986 | 2 |
| #14270985 | 2 |
| #14270983 | 2 |
| #14270973 | 2 |
| C29×#360 | 2 |
| #2230 | 29 |