Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
174 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 55 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×#11745148 | C2 | semidirect |
| 3. C4×Dic116 | C2 | semidirect |
| 4. #14270965 | C2 | semidirect |
| 5. C29×C4⋊C16 | C2 | semidirect |
| 27. Dic116 | D4 | semidirect |
| 53. C4×C29 | SD32 | semidirect |
| 61. C4⋊C16 | D29 | semidirect |
| 77. C29 | #2207 | semidirect |
| 116. C4 | #11745148 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745148 | 2 |
| #14271540 | 2 |
| C4×Dic116 | 2 |
| #14270965 | 2 |
| C29×C4⋊C16 | 2 |
| #2207 | 29 |