Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. #14271507 | C2 | semidirect |
| 4. #14271503 | C2 | semidirect |
| 5. #14271499 | C2 | semidirect |
| 6. #14271496 | C2 | semidirect |
| 7. #14271493 | C2 | semidirect |
| 8. #14271202 | C2 | semidirect |
| 9. #14271170 | C2 | semidirect |
| 11. C29×#483 | C2 | semidirect |
| 32. C29×#106 | C22 | semidirect |
| 33. C29×#103 | C22 | semidirect |
| 35. #11745183 | C22 | semidirect |
| 38. #11745166 | C22 | semidirect |
| 39. #11745164 | C22 | semidirect |
| 40. #11745158 | C22 | semidirect |
| 41. #11745156 | C22 | semidirect |
| 42. #11745155 | C22 | semidirect |
| 141. #483 | D29 | semidirect |
| 174. #106 | C2×D29 | semidirect |
| 178. #103 | C2×D29 | semidirect |
| 182. C29 | #3095 | 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×#11745254 | 2 |
| #14271507 | 2 |
| #14271503 | 2 |
| #14271499 | 2 |
| #14271496 | 2 |
| #14271493 | 2 |
| #14271202 | 2 |
| #14271170 | 2 |
| #14271125 | 2 |
| C29×#483 | 2 |
| #3095 | 29 |