Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14271964 | C2 | semidirect |
| 2. #14271430 | C2 | semidirect |
| 3. #14271330 | C2 | semidirect |
| 4. #14271281 | C2 | semidirect |
| 5. C29×#493 | C2 | semidirect |
| 6. #11745359 | C22 | semidirect |
| 7. C2×D8×C29 | C22 | semidirect |
| 8. C29×#127 | C22 | semidirect |
| 9. #11745294 | C22 | semidirect |
| 14. #11745263 | C22 | semidirect |
| 15. C4×C8×C29 | C22 | semidirect |
| 16. #11745181 | C22 | semidirect |
| 17. #11745167 | C22 | semidirect |
| 18. #11745153 | C22 | semidirect |
| 32. Dic116 | D4 | semidirect |
| 33. D232 | D4 | semidirect |
| 34. #90773 | D4 | semidirect |
| 62. #493 | D29 | semidirect |
| 76. C2×D8 | C2×D29 | semidirect |
| 78. #127 | C2×D29 | semidirect |
| 82. C4×C8 | C2×D29 | semidirect |
| 83. C29 | #3292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271964 | 2 |
| #14271430 | 2 |
| #14271330 | 2 |
| #14271281 | 2 |
| C29×#493 | 2 |
| #3292 | 29 |