Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 135 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. C2×#11745270 | C2 | semidirect |
| 2. C2×#11745311 | C2 | semidirect |
| 3. #14271709 | C2 | semidirect |
| 4. C2×#11745255 | C2 | semidirect |
| 5. #14271381 | C2 | semidirect |
| 6. #14271377 | C2 | semidirect |
| 7. #14271367 | C2 | semidirect |
| 8. #14271357 | C2 | semidirect |
| 9. #14271186 | C2 | semidirect |
| 10. #14271162 | C2 | semidirect |
| 11. C29×#417 | C2 | semidirect |
| 19. #11745309 | C22 | semidirect |
| 20. #11745306 | C22 | semidirect |
| 22. #11745302 | C22 | semidirect |
| 25. #11745298 | C22 | semidirect |
| 39. C29×#103 | C22 | semidirect |
| 40. C29×#102 | C22 | semidirect |
| 41. #11745162 | C22 | semidirect |
| 42. #11745162 | C22 | semidirect |
| 43. #11745158 | C22 | semidirect |
| 44. #11745157 | C22 | semidirect |
| 63. C2×D116 | D4 | semidirect |
| 159. Dic29 | AGL(1,ℤ/8) | semidirect |
| 170. #417 | D29 | semidirect |
| 208. #103 | C2×D29 | semidirect |
| 210. #102 | C2×D29 | semidirect |
| 211. C29 | #3036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745270 | 2 |
| C2×#11745311 | 2 |
| #14271709 | 2 |
| C2×#11745255 | 2 |
| #14271381 | 2 |
| #14271377 | 2 |
| #14271367 | 2 |
| #14271357 | 2 |
| #14271186 | 2 |
| #14271162 | 2 |
| C29×#417 | 2 |
| #3036 | 29 |