Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#11745281 | C2 | semidirect |
| 2. #14271714 | C2 | semidirect |
| 3. C4×#90809 | C2 | semidirect |
| 4. #14271387 | C2 | semidirect |
| 5. #14271381 | C2 | semidirect |
| 6. #14271365 | C2 | semidirect |
| 7. #14271363 | C2 | semidirect |
| 8. #14271359 | C2 | semidirect |
| 9. C4⋊C8×D29 | C2 | semidirect |
| 10. #14271158 | C2 | semidirect |
| 11. C29×#462 | C2 | semidirect |
| 49. #90809 | D4 | semidirect |
| 138. C4×C29 | #135 | semidirect |
| 150. #462 | D29 | semidirect |
| 194. C29 | #3035 | semidirect |
| 292. C4 | #11745281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745281 | 2 |
| #14271714 | 2 |
| C4×#90809 | 2 |
| #14271387 | 2 |
| #14271381 | 2 |
| #14271365 | 2 |
| #14271363 | 2 |
| #14271359 | 2 |
| C4⋊C8×D29 | 2 |
| #14271158 | 2 |
| C29×#462 | 2 |
| #3035 | 29 |