Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
760 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 197 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. C2×#11745236 | C2 | semidirect |
| 3. #14271539 | C2 | direct (N × H) |
| 4. C2×C4×#6597 | C2 | semidirect |
| 5. C2×C29×#127 | C2 | semidirect |
| 11. C29×#127 | C22 | semidirect |
| 14. C2×#90782 | C22 | semidirect |
| 17. #11745236 | C22 | semidirect |
| 18. C4×#6597 | C22 | semidirect |
| 36. C2×#6597 | D4 | semidirect |
| 48. C2×C4×C29 | D8 | semidirect |
| 56. #6597 | C2×D4 | semidirect |
| 68. C4×C29 | C2×D8 | semidirect |
| 72. C2×#127 | D29 | semidirect |
| 76. C2×C29 | #493 | semidirect |
| 90. #127 | C2×D29 | semidirect |
| 93. C29 | C2×#493 | semidirect |
| 126. C2×C4 | #90782 | semidirect |
| 141. C4 | C2×#90782 | semidirect |
| 146. C2 | #14271539 | 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 |
| C2×#11745236 | 2 |
| #14271539 | 2 |
| C2×C4×#6597 | 2 |
| C2×C29×#127 | 2 |
| C2×#493 | 29 |