Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
738 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 153 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×Q8×D29 | C2 | semidirect |
| 2. C2×#11745313 | C2 | semidirect |
| 4. #14271317 | C2 | semidirect |
| 5. #14271300 | C2 | semidirect |
| 6. #14271173 | C2 | semidirect |
| 7. #14271172 | C2 | semidirect |
| 8. #14271126 | C2 | semidirect |
| 9. C2×C29×#137 | C2 | semidirect |
| 21. C2×Q16×C29 | C22 | semidirect |
| 22. C2×SD16×C29 | C22 | semidirect |
| 26. C2×#90785 | C22 | semidirect |
| 30. C2×#90783 | C22 | semidirect |
| 34. #11745183 | C22 | semidirect |
| 36. #11745164 | C22 | semidirect |
| 42. C2×Q8×C29 | D4 | semidirect |
| 66. C2×Dic58 | D4 | semidirect |
| 128. C2×D29 | #137 | semidirect |
| 139. C2×#137 | D29 | semidirect |
| 164. C2×Q16 | C2×D29 | semidirect |
| 166. C2×SD16 | C2×D29 | semidirect |
| 178. C29 | #3004 | semidirect |
| 193. 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×Q8×D29 | 2 |
| C2×#11745313 | 2 |
| #14271670 | 2 |
| #14271317 | 2 |
| #14271300 | 2 |
| #14271173 | 2 |
| #14271172 | 2 |
| #14271126 | 2 |
| C2×C29×#137 | 2 |
| #3004 | 29 |