Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×#11745274 | C2 | semidirect |
| 2. C2×#11745263 | C2 | semidirect |
| 3. #14271742 | C2 | semidirect |
| 4. #14271408 | C2 | semidirect |
| 5. #14271407 | C2 | semidirect |
| 6. #14271405 | C2 | semidirect |
| 7. #14271404 | C2 | semidirect |
| 8. #14271396 | C2 | semidirect |
| 9. #107×D29 | C2 | semidirect |
| 10. #14271161 | C2 | semidirect |
| 11. C29×#466 | C2 | semidirect |
| 80. C8×D29 | D4 | semidirect |
| 145. #466 | D29 | semidirect |
| 184. C29 | #3061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745274 | 2 |
| C2×#11745263 | 2 |
| #14271742 | 2 |
| #14271408 | 2 |
| #14271407 | 2 |
| #14271405 | 2 |
| #14271404 | 2 |
| #14271396 | 2 |
| #107×D29 | 2 |
| #14271161 | 2 |
| C29×#466 | 2 |
| #3061 | 29 |