Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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. C4⋊C8×D29 | C2 | semidirect |
| 3. #14270907 | C2 | semidirect |
| 4. #14270906 | C2 | semidirect |
| 5. C29×#331 | C2 | semidirect |
| 14. C29×C4⋊C8 | C22 | semidirect |
| 16. C4⋊#6597 | C22 | semidirect |
| 75. #331 | D29 | direct (N × H) |
| 80. D29 | #331 | direct (N × H) |
| 91. C4⋊C8 | C2×D29 | semidirect |
| 92. C29 | C2×#331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #127×D29 | 2 |
| C4⋊C8×D29 | 2 |
| #14270907 | 2 |
| #14270906 | 2 |
| C29×#331 | 2 |
| C2×#331 | 29 |