Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
616 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 616 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 |
|---|---|---|
| 1. C22×D232 | C2 | semidirect |
| 2. C22×C8×D29 | C2 | semidirect |
| 3. C2×#11745257 | C2 | semidirect |
| 4. #14271400 | C2 | direct (N × H) |
| 5. C2×#11745157 | C2 | semidirect |
| 6. C2×C29×#107 | C2 | semidirect |
| 15. C2×D232 | C22 | semidirect |
| 17. C2×C8×D29 | C22 | semidirect |
| 19. #11745257 | C22 | semidirect |
| 20. C29×#107 | C22 | semidirect |
| 21. #11745157 | C22 | semidirect |
| 37. C2×C8×C29 | D4 | semidirect |
| 53. C22×D29 | D8 | semidirect |
| 70. C8×C29 | C2×D4 | semidirect |
| 84. C2×D29 | C2×D8 | semidirect |
| 94. C2×#107 | D29 | semidirect |
| 96. C2×C29 | #466 | semidirect |
| 115. #107 | C2×D29 | semidirect |
| 117. C29 | C2×#466 | semidirect |
| 137. C2×C8 | D116 | semidirect |
| 167. C8 | C2×D116 | semidirect |
| 187. C2 | #14271400 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D232 | 2 |
| C22×C8×D29 | 2 |
| C2×#11745257 | 2 |
| #14271400 | 2 |
| C2×#11745157 | 2 |
| C2×C29×#107 | 2 |
| C2×#466 | 29 |