Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
198 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 53 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×#11745148 | C2 | semidirect |
| 2. C2×#11745175 | C2 | semidirect |
| 3. C2×#11745174 | C2 | semidirect |
| 4. #14271546 | C2 | semidirect |
| 5. #14271538 | C2 | semidirect |
| 6. #14270938 | C2 | semidirect |
| 7. C2×C29×D16 | C2 | semidirect |
| 42. C16×C29 | D4 | semidirect |
| 43. #90768 | D4 | semidirect |
| 77. C2×D16 | D29 | semidirect |
| 101. C29 | #2250 | semidirect |
| 122. C16 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745148 | 2 |
| C2×#11745175 | 2 |
| C2×#11745174 | 2 |
| #14271546 | 2 |
| #14271538 | 2 |
| #14270938 | 2 |
| C2×C29×D16 | 2 |
| #2250 | 29 |