Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 145 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. #14271460 | C2 | semidirect |
| 3. #14271450 | C2 | semidirect |
| 4. #14271440 | C2 | semidirect |
| 5. #14271206 | C2 | semidirect |
| 6. #14271187 | C2 | semidirect |
| 8. C29×#533 | C2 | semidirect |
| 11. C29×C4⋊Q8 | C22 | semidirect |
| 12. C29×C4⋊Q8 | C22 | semidirect |
| 13. C29×#125 | C22 | semidirect |
| 29. #11745156 | C22 | semidirect |
| 30. #11745155 | C22 | semidirect |
| 31. C4⋊#6597 | C22 | semidirect |
| 32. C4⋊#6597 | C22 | semidirect |
| 42. C2×D116 | Q8 | semidirect |
| 111. #533 | D29 | semidirect |
| 127. C4⋊Q8 | C2×D29 | semidirect |
| 128. C4⋊Q8 | C2×D29 | semidirect |
| 129. #125 | C2×D29 | semidirect |
| 148. C29 | #3077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D116 | 2 |
| #14271460 | 2 |
| #14271450 | 2 |
| #14271440 | 2 |
| #14271206 | 2 |
| #14271187 | 2 |
| #14271167 | 2 |
| C29×#533 | 2 |
| #3077 | 29 |