Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
160 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 78 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. #14272054 | C2 | semidirect |
| 4. #14272053 | C2 | semidirect |
| 9. C2×#90770 | C4 | semidirect |
| 12. #11745206 | C4 | semidirect |
| 15. C29×M32 | C4 | semidirect |
| 16. #11745160 | C4 | semidirect |
| 18. C16×D29 | C4 | semidirect |
| 76. M32 | #1181 | semidirect |
| 81. C29 | #2110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745206 | 2 |
| #14272126 | 2 |
| #14272054 | 2 |
| #14272053 | 2 |
| M32×D29 | 2 |
| #2110 | 29 |