Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
572 conjugacy classes of subgroups; only the 377 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 377 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 |
|---|---|---|
| 3. #14271121 | C2 | semidirect |
| 4. #14271118 | C2 | semidirect |
| 5. M16×Dic29 | C2 | semidirect |
| 6. C2×C8×Dic29 | C2 | semidirect |
| 9. C29×#131 | C4 | semidirect |
| 12. #11745310 | C4 | semidirect |
| 30. M16×C29 | C2×C4 | semidirect |
| 31. C2×C8×C29 | C2×C4 | semidirect |
| 39. #90777 | C2×C4 | semidirect |
| 40. C2×#6597 | C2×C4 | semidirect |
| 65. Dic29 | #131 | direct (N × H) |
| 78. #131 | Dic29 | direct (N × H) |
| 92. C29 | C4×#131 | semidirect |
| 100. M16 | C2×Dic29 | semidirect |
| 104. C2×C8 | C2×Dic29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745310 | 2 |
| #41×Dic29 | 2 |
| #14271121 | 2 |
| #14271118 | 2 |
| M16×Dic29 | 2 |
| C2×C8×Dic29 | 2 |
| C2×C29×#131 | 2 |
| C4×#131 | 29 |