Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
236 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 57 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. #14271870 | C2 | semidirect |
| 2. #14271535 | C2 | semidirect |
| 3. #14271360 | C2 | semidirect |
| 4. #14270911 | C2 | semidirect |
| 5. #14270893 | C2 | semidirect |
| 6. D4⋊#6597 | C2 | semidirect |
| 58. D4×C29 | SD16 | semidirect |
| 121. C29 | #1622 | semidirect |
| 158. D4 | #90783 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271870 | 2 |
| #14271535 | 2 |
| #14271360 | 2 |
| #14270911 | 2 |
| #14270893 | 2 |
| D4⋊#6597 | 2 |
| C29×#459 | 2 |
| #1622 | 29 |