Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
408 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 408 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 |
|---|---|---|
| 1. C22×#90772 | C2 | semidirect |
| 3. C2×#11745168 | C2 | semidirect |
| 4. C2×#11745168 | C2 | semidirect |
| 5. C2×#11745168 | C2 | semidirect |
| 6. #14270918 | C2 | semidirect |
| 7. C29×#336 | C2 | semidirect |
| 54. C2×C8×C29 | D4 | semidirect |
| 65. C2×#6597 | D4 | semidirect |
| 81. C22×D29 | M16 | semidirect |
| 87. C2×C4×C29 | M16 | semidirect |
| 149. #336 | D29 | semidirect |
| 178. C29 | #1870 | semidirect |
| 213. C2×C8 | D116 | semidirect |
| 254. C2×C4 | #90772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90772 | 2 |
| C2×C4×D116 | 2 |
| C2×#11745168 | 2 |
| #14270918 | 2 |
| C29×#336 | 2 |
| #1870 | 29 |