Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
412 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 145 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. #14271559 | C2 | semidirect |
| 3. #14271535 | C2 | semidirect |
| 4. #14271515 | C2 | semidirect |
| 5. #14271509 | C2 | semidirect |
| 6. #14271390 | C2 | semidirect |
| 7. C4×#90783 | C2 | semidirect |
| 8. C2×C4×#6597 | C2 | semidirect |
| 78. C2×C4×C29 | SD16 | semidirect |
| 90. #6597 | #41 | semidirect |
| 147. C29 | #3167 | semidirect |
| 195. C2×C4 | #90783 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271720 | 2 |
| #14271559 | 2 |
| #14271535 | 2 |
| #14271515 | 2 |
| #14271509 | 2 |
| #14271390 | 2 |
| C4×#90783 | 2 |
| C2×C4×#6597 | 2 |
| C29×#532 | 2 |
| #3167 | 29 |