Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
168 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 168 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 |
|---|---|---|
| 1. #14271293 | C2 | semidirect |
| 3. #14270913 | C2 | semidirect |
| 4. #14270893 | C2 | semidirect |
| 6. #14270884 | C2 | semidirect |
| 56. C8×C29 | SD16 | semidirect |
| 100. C29 | #1582 | semidirect |
| 138. C8 | #90783 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271293 | 2 |
| C4×#90783 | 2 |
| #14270913 | 2 |
| #14270893 | 2 |
| D4⋊#6597 | 2 |
| #14270884 | 2 |
| C8×D4×C29 | 2 |
| #1582 | 29 |