Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11745313 | C2 | semidirect |
| 3. C2×#11745237 | C2 | semidirect |
| 4. #14271385 | C2 | semidirect |
| 5. #14271378 | C2 | semidirect |
| 6. #14271187 | C2 | semidirect |
| 7. #14271171 | C2 | semidirect |
| 8. #14271167 | C2 | semidirect |
| 9. C4×#41×C29 | C2 | semidirect |
| 13. C4×Q8×C29 | C22 | semidirect |
| 15. C4×D4×C29 | C22 | semidirect |
| 22. C2×#90785 | C22 | semidirect |
| 24. C2×#90783 | C22 | semidirect |
| 32. #11745158 | C22 | semidirect |
| 34. C4⋊#6597 | C22 | semidirect |
| 124. C4×#41 | D29 | semidirect |
| 149. C4×Q8 | C2×D29 | semidirect |
| 151. C4×D4 | C2×D29 | semidirect |
| 160. C29 | #3040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745313 | 2 |
| C2×#11745311 | 2 |
| C2×#11745237 | 2 |
| #14271385 | 2 |
| #14271378 | 2 |
| #14271187 | 2 |
| #14271171 | 2 |
| #14271167 | 2 |
| C4×#41×C29 | 2 |
| #3040 | 29 |