Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
400 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 141 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. #14271720 | C2 | semidirect |
| 2. #14271517 | C2 | semidirect |
| 3. #14271513 | C2 | semidirect |
| 4. #14271509 | C2 | semidirect |
| 5. #14271159 | C2 | semidirect |
| 6. C2×C4×#6597 | C2 | semidirect |
| 103. C29 | #3131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271720 | 2 |
| #14271517 | 2 |
| #14271513 | 2 |
| #14271509 | 2 |
| #14271159 | 2 |
| C2×C4×#6597 | 2 |
| C29×#532 | 2 |
| #3131 | 29 |