Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
754 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 754 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 |
|---|---|---|
| 2. C2×#11745304 | C2 | semidirect |
| 3. #14271323 | C2 | semidirect |
| 4. #14271318 | C2 | semidirect |
| 5. #14271313 | C2 | semidirect |
| 6. #14271162 | C2 | semidirect |
| 7. #14271127 | C2 | semidirect |
| 8. C2×C29×C22⋊Q8 | C2 | semidirect |
| 9. C22×Q8×C29 | C22 | semidirect |
| 23. C29×C22⋊Q8 | C22 | semidirect |
| 25. C2×C4⋊C4×C29 | C22 | semidirect |
| 27. C2×#90785 | C22 | semidirect |
| 29. C2×#90784 | C22 | semidirect |
| 30. C2×#90777 | C22 | semidirect |
| 32. C22⋊#6597 | C22 | semidirect |
| 33. #11745158 | C22 | semidirect |
| 34. #11745157 | C22 | semidirect |
| 127. C22×C29 | #137 | semidirect |
| 142. C2×C22⋊Q8 | D29 | semidirect |
| 161. C22×Q8 | C2×D29 | semidirect |
| 173. C22⋊Q8 | C2×D29 | semidirect |
| 175. C2×C4⋊C4 | C2×D29 | semidirect |
| 181. C29 | #3007 | semidirect |
| 277. C22 | #11745304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90805 | 2 |
| C2×#11745304 | 2 |
| #14271323 | 2 |
| #14271318 | 2 |
| #14271313 | 2 |
| #14271162 | 2 |
| #14271127 | 2 |
| C2×C29×C22⋊Q8 | 2 |
| #3007 | 29 |