Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
256 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 256 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 |
|---|---|---|
| 4. #14270910 | C2 | semidirect |
| 5. #14270909 | C2 | semidirect |
| 6. #14270908 | C2 | semidirect |
| 7. C29×#332 | C2 | semidirect |
| 95. #332 | D29 | direct (N × H) |
| 99. D29 | #332 | direct (N × H) |
| 117. C29 | C2×#332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D29 | 2 |
| C4⋊C8×D29 | 2 |
| #14270910 | 2 |
| #14270909 | 2 |
| #14270908 | 2 |
| C29×#332 | 2 |
| C2×#332 | 29 |