Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
464 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 162 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×#11745348 | C2 | semidirect |
| 2. C2×#11745346 | C2 | semidirect |
| 3. #14272208 | C2 | direct (N × H) |
| 4. C2×#11745212 | C2 | semidirect |
| 5. C2×#11745226 | C2 | semidirect |
| 6. C2×#11745224 | C2 | semidirect |
| 7. C2×#11745208 | C2 | semidirect |
| 14. #11745348 | C22 | semidirect |
| 16. #11745346 | C22 | semidirect |
| 23. C2×SD16×C29 | C4 | semidirect |
| 24. C2×#90785 | C4 | semidirect |
| 25. C2×#90782 | C4 | semidirect |
| 26. #11745278 | C4 | semidirect |
| 28. C2×#90773 | C4 | semidirect |
| 30. #11745226 | C22 | semidirect |
| 31. #11745224 | C22 | semidirect |
| 32. #11745212 | C22 | semidirect |
| 33. #11745208 | C22 | semidirect |
| 68. SD16×C29 | C2×C4 | semidirect |
| 70. #90785 | C2×C4 | semidirect |
| 71. #90782 | C2×C4 | semidirect |
| 73. #90773 | C2×C4 | semidirect |
| 136. C2×C29 | #444 | semidirect |
| 147. C2×SD16 | #1181 | semidirect |
| 166. C29 | C2×#444 | semidirect |
| 187. SD16 | C2×#1181 | semidirect |
| 263. C2 | #14272208 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745348 | 2 |
| C2×#11745346 | 2 |
| #14272208 | 2 |
| C2×#11745212 | 2 |
| C2×#11745226 | 2 |
| C2×#11745224 | 2 |
| C2×#11745208 | 2 |
| C2×#11745278 | 2 |
| C2×#444 | 29 |