Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
490 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 490 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×#11745304 | C2 | semidirect |
| 2. C22×#90784 | C2 | semidirect |
| 4. #14271385 | C2 | semidirect |
| 5. #14271363 | C2 | semidirect |
| 6. #14271190 | C2 | semidirect |
| 7. #14271167 | C2 | semidirect |
| 8. #14271157 | C2 | semidirect |
| 9. C29×#519 | C2 | semidirect |
| 14. C4×Q8×C29 | C22 | semidirect |
| 18. C2×#90785 | C22 | semidirect |
| 22. C2×#90784 | C22 | semidirect |
| 29. #11745158 | C22 | semidirect |
| 31. #11745157 | C22 | semidirect |
| 32. C4⋊#6597 | C22 | semidirect |
| 36. C2×Q8×C29 | D4 | semidirect |
| 115. #519 | D29 | semidirect |
| 141. C4×Q8 | C2×D29 | semidirect |
| 149. C29 | #3043 | semidirect |
| 156. C2×Q8 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745304 | 2 |
| C22×#90784 | 2 |
| #14271732 | 2 |
| #14271385 | 2 |
| #14271363 | 2 |
| #14271190 | 2 |
| #14271167 | 2 |
| #14271157 | 2 |
| C29×#519 | 2 |
| #3043 | 29 |