Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
476 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 3. #14271203 | C2 | semidirect |
| 4. #14271202 | C2 | semidirect |
| 5. #14271201 | C2 | semidirect |
| 6. #14271198 | C2 | semidirect |
| 7. #106×D29 | C2 | semidirect |
| 8. C2×C29×#106 | C2 | semidirect |
| 15. #11745263 | C4 | semidirect |
| 38. C2×C8×C29 | C2×C4 | semidirect |
| 50. #90777 | C2×C4 | semidirect |
| 52. #90772 | C2×C4 | semidirect |
| 53. C8×D29 | C2×C4 | semidirect |
| 94. C2×#106 | D29 | semidirect |
| 119. C29 | #2912 | semidirect |
| 133. C2×C8 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745263 | 2 |
| #14271644 | 2 |
| #14271203 | 2 |
| #14271202 | 2 |
| #14271201 | 2 |
| #14271198 | 2 |
| #106×D29 | 2 |
| C2×C29×#106 | 2 |
| #2912 | 29 |