Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
608 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 205 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. C2×C4×D116 | C2 | semidirect |
| 3. #14271276 | C2 | direct (N × H) |
| 4. C2×#11745165 | C2 | semidirect |
| 5. C2×#11745169 | C2 | semidirect |
| 6. C2×C29×#97 | C2 | semidirect |
| 14. C2×D232 | C4 | semidirect |
| 17. C4×D116 | C22 | semidirect |
| 18. C29×#97 | C22 | semidirect |
| 19. #11745169 | C22 | semidirect |
| 20. #11745165 | C22 | semidirect |
| 27. C2×D116 | C2×C4 | semidirect |
| 32. C2×C8×C29 | C2×C4 | semidirect |
| 40. D232 | C2×C4 | semidirect |
| 56. D116 | C22×C4 | semidirect |
| 59. C8×C29 | C22×C4 | semidirect |
| 78. C2×#97 | D29 | semidirect |
| 79. C2×C29 | #442 | semidirect |
| 96. #97 | C2×D29 | semidirect |
| 97. C29 | C2×#442 | semidirect |
| 110. C2×C8 | C4×D29 | semidirect |
| 136. C8 | C2×C4×D29 | semidirect |
| 150. C2 | #14271276 | 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 |
| C2×C4×D116 | 2 |
| #14271276 | 2 |
| C2×#11745165 | 2 |
| C2×#11745169 | 2 |
| C2×C29×#97 | 2 |
| C2×#442 | 29 |