Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
564 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 181 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×#90773 | C2 | semidirect |
| 2. C2×#11745286 | C2 | semidirect |
| 4. #14271392 | C2 | direct (N × H) |
| 5. C2×#11745165 | C2 | semidirect |
| 6. C2×#11745164 | C2 | semidirect |
| 7. C2×#11745169 | C2 | semidirect |
| 8. C23×C8×C29 | C2 | semidirect |
| 16. C22×C8×C29 | C22 | semidirect |
| 24. #11745286 | C22 | semidirect |
| 27. C2×#90773 | C22 | semidirect |
| 28. #11745169 | C22 | semidirect |
| 29. #11745165 | C22 | semidirect |
| 30. #11745164 | C22 | semidirect |
| 54. C2×C8×C29 | D4 | semidirect |
| 67. C23×C29 | SD16 | semidirect |
| 97. C8×C29 | C2×D4 | semidirect |
| 104. C22×C29 | C2×SD16 | semidirect |
| 119. C23×C8 | D29 | semidirect |
| 127. C2×C29 | #465 | semidirect |
| 141. C22×C8 | C2×D29 | semidirect |
| 154. C29 | C2×#465 | semidirect |
| 179. C2×C8 | C22⋊D29 | semidirect |
| 195. C23 | #90773 | semidirect |
| 221. C8 | C2×C22⋊D29 | semidirect |
| 230. C22 | C2×#90773 | semidirect |
| 243. C2 | #14271392 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90773 | 2 |
| C2×#11745286 | 2 |
| C2×#11745292 | 2 |
| #14271392 | 2 |
| C2×#11745165 | 2 |
| C2×#11745164 | 2 |
| C2×#11745169 | 2 |
| C23×C8×C29 | 2 |
| C2×#465 | 29 |