Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
346 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #14271637 | C2 | semidirect |
| 3. #14271169 | C2 | semidirect |
| 4. #14271137 | C2 | semidirect |
| 5. #14270935 | C2 | semidirect |
| 6. #14270919 | C2 | semidirect |
| 7. C29×#421 | C2 | semidirect |
| 14. C2×#90784 | C4 | semidirect |
| 15. C2×#90782 | C4 | semidirect |
| 30. C2×Q8×C29 | C2×C4 | semidirect |
| 32. C2×D4×C29 | C2×C4 | semidirect |
| 59. C2×#6597 | C2×C4 | semidirect |
| 112. #421 | D29 | semidirect |
| 140. C29 | #1904 | semidirect |
| 146. C2×Q8 | C4×D29 | semidirect |
| 154. C2×D4 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745311 | 2 |
| #14271637 | 2 |
| #14271169 | 2 |
| #14271137 | 2 |
| #14270935 | 2 |
| #14270919 | 2 |
| C29×#421 | 2 |
| #1904 | 29 |