Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
154 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 154 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 |
|---|---|---|
| 2. #14271276 | C2 | semidirect |
| 3. #14270987 | C2 | semidirect |
| 4. #14270975 | C2 | semidirect |
| 5. #14270973 | C2 | semidirect |
| 6. #14270941 | C2 | semidirect |
| 7. C29×#444 | C2 | semidirect |
| 15. #11745176 | C4 | semidirect |
| 16. #11745174 | C4 | semidirect |
| 24. Q16×C29 | C2×C4 | semidirect |
| 26. D8×C29 | C2×C4 | semidirect |
| 38. #90768 | C2×C4 | semidirect |
| 66. #444 | D29 | semidirect |
| 89. C29 | AGL(1,ℤ/16) | semidirect |
| 93. Q16 | C4×D29 | semidirect |
| 97. D8 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271598 | 2 |
| #14271276 | 2 |
| #14270987 | 2 |
| #14270975 | 2 |
| #14270973 | 2 |
| #14270941 | 2 |
| C29×#444 | 2 |
| AGL(1,ℤ/16) | 29 |