Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 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. #14271887 | C2 | semidirect |
| 3. #14271500 | C2 | semidirect |
| 4. #14271490 | C2 | semidirect |
| 5. #14271445 | C2 | semidirect |
| 6. #14271440 | C2 | semidirect |
| 7. #14271410 | C2 | semidirect |
| 8. C4×#90773 | C2 | semidirect |
| 9. #14271242 | C2 | semidirect |
| 10. #14271204 | C2 | semidirect |
| 11. C29×#500 | C2 | semidirect |
| 98. C8×C29 | #41 | semidirect |
| 120. #500 | D29 | semidirect |
| 163. C29 | #3353 | semidirect |
| 222. C8 | #90809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271887 | 2 |
| #14271816 | 2 |
| #14271500 | 2 |
| #14271490 | 2 |
| #14271445 | 2 |
| #14271440 | 2 |
| #14271410 | 2 |
| C4×#90773 | 2 |
| #14271242 | 2 |
| #14271204 | 2 |
| C29×#500 | 2 |
| #3353 | 29 |