Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×#11745294 | C2 | semidirect |
| 2. #14271713 | C2 | semidirect |
| 3. #14271550 | C2 | semidirect |
| 4. #14271539 | C2 | semidirect |
| 5. #14271535 | C2 | semidirect |
| 6. C4×#90777 | C2 | semidirect |
| 7. C2×C29×#127 | C2 | semidirect |
| 15. C2×#90783 | C22 | semidirect |
| 17. C2×#90782 | C22 | semidirect |
| 20. #11745237 | C22 | semidirect |
| 21. #11745236 | C22 | semidirect |
| 23. #11745231 | C22 | semidirect |
| 24. #11745151 | C22 | semidirect |
| 25. C4×#6597 | C22 | semidirect |
| 48. #90777 | D4 | semidirect |
| 71. #6597 | C2×D4 | semidirect |
| 83. C4×C29 | AGL(1,ℤ/8) | semidirect |
| 88. C2×#127 | D29 | semidirect |
| 116. C29 | #3151 | semidirect |
| 173. C4 | #11745294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745294 | 2 |
| #14271713 | 2 |
| #14271550 | 2 |
| #14271539 | 2 |
| #14271535 | 2 |
| C4×#90777 | 2 |
| C2×C29×#127 | 2 |
| #3151 | 29 |