Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×#11745271 | C2 | semidirect |
| 2. C2×#11745269 | C2 | semidirect |
| 4. #14271739 | C2 | semidirect |
| 5. #14271422 | C2 | semidirect |
| 6. #14271410 | C2 | semidirect |
| 7. #14271405 | C2 | semidirect |
| 8. #14271393 | C2 | semidirect |
| 9. #14271157 | C2 | semidirect |
| 10. C2×#11745158 | C2 | semidirect |
| 11. C29×#428 | C2 | semidirect |
| 63. M16×C29 | D4 | semidirect |
| 146. #428 | D29 | semidirect |
| 186. C29 | #3063 | semidirect |
| 210. M16 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745271 | 2 |
| C2×#11745269 | 2 |
| #14271744 | 2 |
| #14271739 | 2 |
| #14271422 | 2 |
| #14271410 | 2 |
| #14271405 | 2 |
| #14271393 | 2 |
| #14271157 | 2 |
| C2×#11745158 | 2 |
| C29×#428 | 2 |
| #3063 | 29 |