Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
764 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 141 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×#90809 | C2 | semidirect |
| 2. C2×#11745281 | C2 | semidirect |
| 3. #14271676 | C2 | semidirect |
| 4. #14271324 | C2 | semidirect |
| 5. #14271313 | C2 | semidirect |
| 6. #14271311 | C2 | semidirect |
| 7. #14271302 | C2 | semidirect |
| 8. #14271299 | C2 | semidirect |
| 9. #14271158 | C2 | semidirect |
| 10. C22⋊C8×D29 | C2 | semidirect |
| 11. C29×#451 | C2 | semidirect |
| 18. C2×#90809 | C22 | semidirect |
| 23. C2×Q16×C29 | C22 | semidirect |
| 25. #11745308 | C22 | semidirect |
| 26. C2×#90784 | C22 | semidirect |
| 27. C2×#90784 | C22 | semidirect |
| 30. C2×D232 | C22 | semidirect |
| 31. C2×C8×D29 | C22 | semidirect |
| 32. #11745257 | C22 | semidirect |
| 35. #11745254 | C22 | semidirect |
| 38. C29×#103 | C22 | semidirect |
| 40. #11745183 | C22 | semidirect |
| 42. #11745169 | C22 | semidirect |
| 43. #11745168 | C22 | semidirect |
| 44. #11745157 | C22 | semidirect |
| 61. #90809 | D4 | semidirect |
| 144. C22×C29 | #135 | semidirect |
| 172. #451 | D29 | semidirect |
| 199. C2×Q16 | C2×D29 | semidirect |
| 214. #103 | C2×D29 | semidirect |
| 220. C29 | #3002 | semidirect |
| 333. C22 | #11745281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90809 | 2 |
| C2×#11745281 | 2 |
| #14271676 | 2 |
| #14271324 | 2 |
| #14271313 | 2 |
| #14271311 | 2 |
| #14271302 | 2 |
| #14271299 | 2 |
| #14271158 | 2 |
| C22⋊C8×D29 | 2 |
| C29×#451 | 2 |
| #3002 | 29 |