Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
182 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 182 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. #14271511 | C2 | semidirect |
| 3. D4×#6597 | C2 | semidirect |
| 4. #14270915 | C2 | semidirect |
| 5. #14270909 | C2 | semidirect |
| 6. #14270906 | C2 | semidirect |
| 7. C29×#461 | C2 | semidirect |
| 81. #461 | D29 | semidirect |
| 107. C29 | #1681 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271511 | 2 |
| #14271358 | 2 |
| D4×#6597 | 2 |
| #14270915 | 2 |
| #14270909 | 2 |
| #14270906 | 2 |
| C29×#461 | 2 |
| #1681 | 29 |