Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
456 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 217 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×#11745310 | C2 | semidirect |
| 2. #14271285 | C2 | semidirect |
| 3. #14271280 | C2 | semidirect |
| 4. #14271212 | C2 | semidirect |
| 5. #14271180 | C2 | semidirect |
| 6. #14271121 | C2 | semidirect |
| 9. C29×#137 | C4 | semidirect |
| 10. C29×AGL(1,ℤ/8) | C4 | semidirect |
| 15. #11745310 | C22 | semidirect |
| 16. #11745310 | C22 | semidirect |
| 22. #11745185 | C22 | semidirect |
| 23. #11745167 | C22 | semidirect |
| 24. #11745163 | C22 | semidirect |
| 25. C8×Dic29 | C22 | semidirect |
| 98. #137 | Dic29 | semidirect |
| 99. AGL(1,ℤ/8) | Dic29 | semidirect |
| 115. C29 | #2955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745310 | 2 |
| #14271285 | 2 |
| #14271280 | 2 |
| #14271212 | 2 |
| #14271180 | 2 |
| #14271121 | 2 |
| C29×#575 | 2 |
| #2955 | 29 |