Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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×#90784 | C2 | semidirect |
| 3. C2×#11745308 | C2 | semidirect |
| 4. #14271324 | C2 | direct (N × H) |
| 5. C2×#11745183 | C2 | semidirect |
| 6. C2×#11745169 | C2 | semidirect |
| 7. C2×#11745168 | C2 | semidirect |
| 8. C22×Q16×C29 | C2 | semidirect |
| 20. C2×Q16×C29 | C22 | semidirect |
| 23. #11745308 | C22 | semidirect |
| 25. C2×#90784 | C22 | semidirect |
| 30. #11745183 | C22 | semidirect |
| 31. #11745169 | C22 | semidirect |
| 32. #11745168 | C22 | semidirect |
| 131. C22×Q16 | D29 | semidirect |
| 138. C2×C29 | #452 | semidirect |
| 155. C2×Q16 | C2×D29 | semidirect |
| 168. C29 | C2×#452 | semidirect |
| 267. C2 | #14271324 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90809 | 2 |
| C22×#90784 | 2 |
| C2×#11745308 | 2 |
| #14271324 | 2 |
| C2×#11745183 | 2 |
| C2×#11745169 | 2 |
| C2×#11745168 | 2 |
| C22×Q16×C29 | 2 |
| C2×#452 | 29 |