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×#11745271 | C2 | semidirect |
| 3. C2×#11745304 | C2 | semidirect |
| 5. #14271320 | C2 | semidirect |
| 6. #14271303 | C2 | semidirect |
| 7. #14271171 | C2 | semidirect |
| 8. #14271126 | C2 | semidirect |
| 9. C29×#419 | C2 | semidirect |
| 22. C2×#90785 | C22 | semidirect |
| 24. C2×#90784 | C22 | semidirect |
| 27. C2×Dic116 | C22 | semidirect |
| 28. C2×#90773 | C22 | semidirect |
| 34. C29×#103 | C22 | semidirect |
| 36. #11745158 | C22 | semidirect |
| 40. C2×Q8×C29 | D4 | semidirect |
| 65. C2×Dic58 | D4 | semidirect |
| 128. C2×D29 | #137 | semidirect |
| 144. #419 | D29 | semidirect |
| 176. #103 | C2×D29 | semidirect |
| 178. C29 | #3004 | semidirect |
| 194. C2×Q8 | D116 | 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×#11745271 | 2 |
| C2×#11745304 | 2 |
| #14271675 | 2 |
| #14271320 | 2 |
| #14271303 | 2 |
| #14271171 | 2 |
| #14271126 | 2 |
| C29×#419 | 2 |
| #3004 | 29 |