Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
230 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 230 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×#11745281 | C2 | semidirect |
| 2. C2×#11745176 | C2 | semidirect |
| 3. C2×D464 | C2 | semidirect |
| 4. #14271400 | C2 | semidirect |
| 5. #14270963 | C2 | semidirect |
| 6. #14270942 | C2 | semidirect |
| 7. C29×#358 | C2 | semidirect |
| 33. Q16×C29 | D4 | semidirect |
| 42. D232 | D4 | semidirect |
| 88. #358 | D29 | semidirect |
| 112. C29 | #2186 | semidirect |
| 123. Q16 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745281 | 2 |
| C2×#11745176 | 2 |
| C2×D464 | 2 |
| #14271400 | 2 |
| #14270963 | 2 |
| #14270942 | 2 |
| C29×#358 | 2 |
| #2186 | 29 |