Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
306 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 2. C2×#11745153 | C2 | semidirect |
| 3. #14271165 | C2 | semidirect |
| 4. #14271164 | C2 | semidirect |
| 5. #14271033 | C2 | semidirect |
| 6. #14270931 | C2 | semidirect |
| 7. C2×C29×#104 | C2 | semidirect |
| 52. C42×C29 | D4 | semidirect |
| 124. C2×#104 | D29 | semidirect |
| 155. C29 | #2039 | semidirect |
| 192. C42 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271741 | 2 |
| C2×#11745153 | 2 |
| #14271165 | 2 |
| #14271164 | 2 |
| #14271033 | 2 |
| #14270931 | 2 |
| C2×C29×#104 | 2 |
| #2039 | 29 |