Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
520 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 157 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×#11745266 | C2 | semidirect |
| 2. #14271674 | C2 | semidirect |
| 3. #14271404 | C2 | semidirect |
| 4. #14271399 | C2 | semidirect |
| 5. #14271392 | C2 | semidirect |
| 6. #14271201 | C2 | semidirect |
| 7. #14271160 | C2 | semidirect |
| 8. C23×C8×C29 | C2 | semidirect |
| 22. C2×Dic116 | C22 | semidirect |
| 24. C2×D232 | C22 | semidirect |
| 25. C2×#90773 | C22 | semidirect |
| 26. #11745169 | C22 | semidirect |
| 27. #11745166 | C22 | semidirect |
| 28. #11745165 | C22 | semidirect |
| 29. #11745164 | C22 | semidirect |
| 47. C2×C8×C29 | D4 | semidirect |
| 92. C22×C29 | #135 | semidirect |
| 103. C23×C8 | D29 | semidirect |
| 136. C29 | #3050 | semidirect |
| 157. C2×C8 | C22⋊D29 | semidirect |
| 199. C22 | #11745266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745266 | 2 |
| #14271674 | 2 |
| #14271404 | 2 |
| #14271399 | 2 |
| #14271392 | 2 |
| #14271201 | 2 |
| #14271160 | 2 |
| C23×C8×C29 | 2 |
| #3050 | 29 |