Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
216 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 56 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. #14272178 | C2 | semidirect |
| 4. M16×#1181 | C2 | semidirect |
| 5. #14272046 | C2 | semidirect |
| 6. #14272035 | C2 | semidirect |
| 23. C29×#100 | C4 | semidirect |
| 24. #11745181 | C4 | semidirect |
| 25. #11745172 | C4 | semidirect |
| 26. #11745172 | C4 | semidirect |
| 129. #100 | #1181 | semidirect |
| 132. C29 | #1932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272178 | 2 |
| #14272161 | 2 |
| C2×#11745224 | 2 |
| M16×#1181 | 2 |
| #14272046 | 2 |
| #14272035 | 2 |
| #14271144 | 2 |
| #1932 | 29 |