Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14271886 | C2 | semidirect |
| 3. #14271510 | C2 | semidirect |
| 4. #14271490 | C2 | semidirect |
| 5. #14271448 | C2 | semidirect |
| 6. #14271395 | C2 | semidirect |
| 7. #14271363 | C2 | semidirect |
| 8. #14271324 | C2 | semidirect |
| 9. C8×D116 | C2 | semidirect |
| 10. #14271158 | C2 | semidirect |
| 11. C4×Q16×C29 | C2 | semidirect |
| 131. C4×Q16 | D29 | semidirect |
| 168. C29 | #3304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271886 | 2 |
| #14271835 | 2 |
| #14271510 | 2 |
| #14271490 | 2 |
| #14271448 | 2 |
| #14271395 | 2 |
| #14271363 | 2 |
| #14271324 | 2 |
| C8×D116 | 2 |
| #14271158 | 2 |
| C4×Q16×C29 | 2 |
| #3304 | 29 |