Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
320 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. M16×Dic29 | C2 | semidirect |
| 5. #14271009 | C2 | semidirect |
| 6. #14270922 | C2 | semidirect |
| 7. C29×#339 | C2 | semidirect |
| 15. #11745255 | C4 | semidirect |
| 16. #11745249 | C4 | semidirect |
| 21. #11745173 | C4 | semidirect |
| 24. #11745153 | C4 | semidirect |
| 39. M16×C29 | C2×C4 | semidirect |
| 45. C42×C29 | C2×C4 | semidirect |
| 51. C4×Dic29 | C2×C4 | semidirect |
| 55. #90777 | C2×C4 | semidirect |
| 108. #339 | D29 | semidirect |
| 131. C29 | #1759 | semidirect |
| 148. M16 | C4×D29 | semidirect |
| 163. C42 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271631 | 2 |
| C2×#11745153 | 2 |
| C2×#11745173 | 2 |
| M16×Dic29 | 2 |
| #14271009 | 2 |
| #14270922 | 2 |
| C29×#339 | 2 |
| #1759 | 29 |