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×#11745313 | C2 | semidirect |
| 2. C2×#11745310 | C2 | semidirect |
| 3. #14271734 | C2 | semidirect |
| 4. #14271419 | C2 | semidirect |
| 5. #14271407 | C2 | semidirect |
| 6. #14271402 | C2 | semidirect |
| 7. #14271390 | C2 | semidirect |
| 8. #14271203 | C2 | semidirect |
| 9. #14271159 | C2 | semidirect |
| 10. C2×#11745158 | C2 | semidirect |
| 79. #90777 | D4 | semidirect |
| 186. C29 | #3063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745313 | 2 |
| C2×#11745310 | 2 |
| #14271734 | 2 |
| #14271419 | 2 |
| #14271407 | 2 |
| #14271402 | 2 |
| #14271390 | 2 |
| #14271203 | 2 |
| #14271159 | 2 |
| C2×#11745158 | 2 |
| C29×#537 | 2 |
| #3063 | 29 |