Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 758 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. C22×#90809 | C2 | semidirect |
| 2. C2×#11745311 | C2 | semidirect |
| 3. #14271670 | C2 | semidirect |
| 4. #14271324 | C2 | semidirect |
| 5. #14271307 | C2 | semidirect |
| 6. #14271172 | C2 | semidirect |
| 7. #14271169 | C2 | semidirect |
| 8. #14271126 | C2 | semidirect |
| 9. C2×C29×#137 | C2 | semidirect |
| 21. C2×Q16×C29 | C22 | semidirect |
| 22. C2×SD16×C29 | C22 | semidirect |
| 25. #11745308 | C22 | semidirect |
| 26. C2×#90784 | C22 | semidirect |
| 27. #11745300 | C22 | semidirect |
| 30. C2×#90782 | C22 | semidirect |
| 34. #11745183 | C22 | semidirect |
| 35. #11745169 | C22 | semidirect |
| 36. #11745168 | C22 | semidirect |
| 43. C2×Q8×C29 | D4 | semidirect |
| 60. C2×D116 | D4 | semidirect |
| 141. C2×#137 | D29 | semidirect |
| 167. C2×Q16 | C2×D29 | semidirect |
| 169. C2×SD16 | C2×D29 | semidirect |
| 182. C29 | #3005 | semidirect |
| 192. C2×Q8 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90809 | 2 |
| C2×#11745311 | 2 |
| #14271670 | 2 |
| #14271324 | 2 |
| #14271307 | 2 |
| #14271172 | 2 |
| #14271169 | 2 |
| #14271126 | 2 |
| C2×C29×#137 | 2 |
| #3005 | 29 |