Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
480 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D29 | C2 | semidirect |
| 4. #14271374 | C2 | semidirect |
| 5. #14271372 | C2 | semidirect |
| 6. #14271370 | C2 | semidirect |
| 7. #14271368 | C2 | semidirect |
| 8. #14271366 | C2 | semidirect |
| 9. #14271185 | C2 | semidirect |
| 10. #14271170 | C2 | semidirect |
| 11. C29×#461 | C2 | semidirect |
| 132. C4×C29 | #137 | semidirect |
| 140. Dic29 | #137 | semidirect |
| 149. #461 | D29 | semidirect |
| 189. C29 | #3039 | semidirect |
| 283. C4 | #11745277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745277 | 2 |
| C4⋊Q8×D29 | 2 |
| C4×#90807 | 2 |
| #14271374 | 2 |
| #14271372 | 2 |
| #14271370 | 2 |
| #14271368 | 2 |
| #14271366 | 2 |
| #14271185 | 2 |
| #14271170 | 2 |
| C29×#461 | 2 |
| #3039 | 29 |