Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 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×#11745263 | C2 | semidirect |
| 2. #14271741 | C2 | semidirect |
| 3. #14271406 | C2 | semidirect |
| 4. #14271401 | C2 | semidirect |
| 5. #14271396 | C2 | semidirect |
| 6. C2×#11745166 | C2 | semidirect |
| 7. #14271164 | C2 | semidirect |
| 8. C2×C29×#135 | C2 | semidirect |
| 48. C2×C8×C29 | D4 | semidirect |
| 103. C2×#135 | D29 | semidirect |
| 138. C29 | #3061 | semidirect |
| 161. 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×#11745263 | 2 |
| #14271741 | 2 |
| #14271406 | 2 |
| #14271401 | 2 |
| #14271396 | 2 |
| C2×#11745166 | 2 |
| #14271164 | 2 |
| C2×C29×#135 | 2 |
| #3061 | 29 |