Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
616 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 173 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×#90782 | C2 | semidirect |
| 2. C23×#6597 | C2 | semidirect |
| 3. C2×#11745292 | C2 | semidirect |
| 4. #14271397 | C2 | direct (N × H) |
| 5. C2×#11745155 | C2 | semidirect |
| 6. C2×#11745180 | C2 | semidirect |
| 7. C2×#11745157 | C2 | semidirect |
| 8. C2×C29×#121 | C2 | semidirect |
| 15. C29×#121 | C22 | semidirect |
| 19. C2×#90782 | C22 | semidirect |
| 21. #11745292 | C22 | semidirect |
| 27. C22×#6597 | C22 | semidirect |
| 28. #11745180 | C22 | semidirect |
| 29. #11745157 | C22 | semidirect |
| 30. #11745155 | C22 | semidirect |
| 63. C2×#6597 | D4 | semidirect |
| 72. C23×C29 | D8 | semidirect |
| 101. #6597 | C2×D4 | semidirect |
| 112. C22×C29 | C2×D8 | semidirect |
| 128. C2×#121 | D29 | semidirect |
| 135. C2×C29 | #466 | semidirect |
| 154. #121 | C2×D29 | semidirect |
| 162. C29 | C2×#466 | semidirect |
| 208. C23 | #90782 | semidirect |
| 246. C22 | C2×#90782 | semidirect |
| 259. C2 | #14271397 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90782 | 2 |
| C23×#6597 | 2 |
| C2×#11745292 | 2 |
| #14271397 | 2 |
| C2×#11745155 | 2 |
| C2×#11745180 | 2 |
| C2×#11745157 | 2 |
| C2×C29×#121 | 2 |
| C2×#466 | 29 |