Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
216 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 77 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. #14271212 | C2 | semidirect |
| 4. M16×Dic29 | C2 | semidirect |
| 5. #14270935 | C2 | semidirect |
| 6. #14270924 | C2 | semidirect |
| 15. C29×#101 | C4 | semidirect |
| 16. C29×#100 | C4 | semidirect |
| 114. #101 | Dic29 | semidirect |
| 115. #100 | Dic29 | semidirect |
| 118. C29 | #1932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271212 | 2 |
| #14271180 | 2 |
| C2×#11745185 | 2 |
| M16×Dic29 | 2 |
| #14270935 | 2 |
| #14270924 | 2 |
| C29×#413 | 2 |
| #1932 | 29 |