Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
174 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 51 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×#11745176 | C2 | semidirect |
| 3. Q16×Dic29 | C2 | semidirect |
| 4. #14270981 | C2 | semidirect |
| 5. #14270965 | C2 | semidirect |
| 6. #14270964 | C2 | semidirect |
| 7. C2×C29×SD32 | C2 | semidirect |
| 27. Q16×C29 | D4 | semidirect |
| 72. Dic29 | SD32 | semidirect |
| 74. C2×SD32 | D29 | semidirect |
| 98. C29 | #2207 | semidirect |
| 105. Q16 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745176 | 2 |
| #14271538 | 2 |
| Q16×Dic29 | 2 |
| #14270981 | 2 |
| #14270965 | 2 |
| #14270964 | 2 |
| C2×C29×SD32 | 2 |
| #2207 | 29 |