Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11745266 | C2 | semidirect |
| 2. C2×#11745312 | C2 | semidirect |
| 3. #14271709 | C2 | semidirect |
| 4. #14271556 | C2 | semidirect |
| 5. #14271554 | C2 | semidirect |
| 6. #14271551 | C2 | semidirect |
| 7. #14271549 | C2 | semidirect |
| 8. C2×#11745163 | C2 | semidirect |
| 9. C2×C29×#135 | C2 | semidirect |
| 54. C2×C8×C29 | D4 | semidirect |
| 66. C2×#6597 | D4 | semidirect |
| 114. C2×#135 | D29 | semidirect |
| 152. C29 | #3150 | semidirect |
| 180. C2×C8 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745266 | 2 |
| C2×#11745312 | 2 |
| #14271709 | 2 |
| #14271556 | 2 |
| #14271554 | 2 |
| #14271551 | 2 |
| #14271549 | 2 |
| C2×#11745163 | 2 |
| C2×C29×#135 | 2 |
| #3150 | 29 |