Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
342 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 79 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. #14271929 | C2 | semidirect |
| 3. #14271145 | C2 | semidirect |
| 4. #14271127 | C2 | semidirect |
| 5. #14270935 | C2 | semidirect |
| 6. #14270934 | C2 | semidirect |
| 7. C29×#407 | C2 | semidirect |
| 50. C2×C8×C29 | D4 | semidirect |
| 62. C2×#6597 | D4 | semidirect |
| 124. #407 | D29 | semidirect |
| 152. C29 | #1891 | semidirect |
| 184. C2×C8 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271929 | 2 |
| #14271674 | 2 |
| #14271145 | 2 |
| #14271127 | 2 |
| #14270935 | 2 |
| #14270934 | 2 |
| C29×#407 | 2 |
| #1891 | 29 |