Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
480 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 183 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 |
|---|---|---|
| 3. #14271271 | C2 | semidirect |
| 4. #14271270 | C2 | semidirect |
| 5. #14271269 | C2 | semidirect |
| 6. #14271268 | C2 | semidirect |
| 7. #14271267 | C2 | semidirect |
| 11. C29×#441 | C2 | semidirect |
| 17. Q16×D29 | C4 | semidirect |
| 49. Q16×C29 | C2×C4 | semidirect |
| 56. #90785 | C2×C4 | semidirect |
| 69. Dic116 | C2×C4 | semidirect |
| 115. #441 | D29 | direct (N × H) |
| 121. D29 | #441 | direct (N × H) |
| 150. C29 | C2×#441 | semidirect |
| 162. Q16 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D29 | 2 |
| C4×Q8×D29 | 2 |
| #14271271 | 2 |
| #14271270 | 2 |
| #14271269 | 2 |
| #14271268 | 2 |
| #14271267 | 2 |
| #106×D29 | 2 |
| #103×D29 | 2 |
| #97×D29 | 2 |
| C29×#441 | 2 |
| C2×#441 | 29 |