Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1008 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 229 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. C22×#90772 | C2 | semidirect |
| 3. C2×#11745254 | C2 | semidirect |
| 4. #14271166 | C2 | direct (N × H) |
| 5. C2×#11745169 | C2 | semidirect |
| 6. C2×#11745180 | C2 | semidirect |
| 7. C2×#11745157 | C2 | semidirect |
| 8. C2×C29×#102 | C2 | semidirect |
| 14. C2×D4×D29 | C4 | semidirect |
| 18. C22×C8×C29 | C22 | semidirect |
| 19. C2×C4⋊C4×C29 | C22 | semidirect |
| 21. C2×C4⋊Dic29 | C22 | semidirect |
| 23. C22×#6597 | C22 | semidirect |
| 25. C2×#90772 | C22 | semidirect |
| 27. #11745254 | C22 | semidirect |
| 28. C29×#102 | C22 | semidirect |
| 29. #11745180 | C22 | semidirect |
| 30. #11745169 | C22 | semidirect |
| 31. #11745157 | C22 | semidirect |
| 51. D4×D29 | C2×C4 | semidirect |
| 61. C2×C8×C29 | C23 | semidirect |
| 63. C4⋊C4×C29 | C23 | semidirect |
| 66. C4⋊Dic29 | C23 | semidirect |
| 69. C2×#6597 | C23 | semidirect |
| 141. C2×#102 | D29 | semidirect |
| 143. C2×C29 | #418 | semidirect |
| 161. C22×C8 | C2×D29 | semidirect |
| 165. C2×C4⋊C4 | C2×D29 | semidirect |
| 171. #102 | C2×D29 | semidirect |
| 172. C29 | C2×#418 | semidirect |
| 205. C2×C8 | C22×D29 | semidirect |
| 209. C4⋊C4 | C22×D29 | semidirect |
| 277. C2 | #14271166 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D29 | 2 |
| C22×#90772 | 2 |
| C2×#11745254 | 2 |
| #14271166 | 2 |
| C2×#11745169 | 2 |
| C2×#11745180 | 2 |
| C2×#11745157 | 2 |
| C2×C29×#102 | 2 |
| C2×#418 | 29 |