Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
340 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 1. #14271929 | C2 | semidirect |
| 3. #14271145 | C2 | semidirect |
| 4. C2×#11745171 | C2 | semidirect |
| 5. C2×#11745171 | C2 | semidirect |
| 6. #14270933 | C2 | semidirect |
| 7. C29×#344 | C2 | semidirect |
| 46. M16×C29 | D4 | semidirect |
| 56. #90777 | D4 | semidirect |
| 115. #344 | D29 | semidirect |
| 140. C29 | #1914 | semidirect |
| 166. M16 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271929 | 2 |
| #14271732 | 2 |
| #14271145 | 2 |
| C2×#11745171 | 2 |
| #14270933 | 2 |
| C29×#344 | 2 |
| #1914 | 29 |