Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
422 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 161 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. #14271236 | C2 | semidirect |
| 3. #14271233 | C2 | semidirect |
| 4. C8×D116 | C2 | semidirect |
| 5. #14271228 | C2 | semidirect |
| 6. #14271224 | C2 | semidirect |
| 7. #14271128 | C2 | semidirect |
| 8. C22⋊C8×D29 | C2 | semidirect |
| 9. C29×#433 | C2 | semidirect |
| 13. C2×#90772 | C22 | semidirect |
| 16. C2×C8×D29 | C22 | semidirect |
| 23. C29×C4⋊C8 | C22 | semidirect |
| 25. C29×#97 | C22 | semidirect |
| 26. C4×C8×C29 | C22 | semidirect |
| 30. #11745168 | C22 | semidirect |
| 31. #11745168 | C22 | semidirect |
| 32. C4⋊#6597 | C22 | semidirect |
| 33. #11745151 | C22 | semidirect |
| 34. C4×#6597 | C22 | semidirect |
| 116. #433 | D29 | semidirect |
| 138. C4⋊C8 | C2×D29 | semidirect |
| 146. #97 | C2×D29 | semidirect |
| 148. C4×C8 | C2×D29 | semidirect |
| 149. C29 | #2977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271675 | 2 |
| #14271236 | 2 |
| #14271233 | 2 |
| C8×D116 | 2 |
| #14271228 | 2 |
| #14271224 | 2 |
| #14271128 | 2 |
| C22⋊C8×D29 | 2 |
| C29×#433 | 2 |
| #2977 | 29 |