Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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. #14271883 | C2 | semidirect |
| 3. #14271514 | C2 | semidirect |
| 4. #14271505 | C2 | semidirect |
| 5. #14271444 | C2 | semidirect |
| 6. #14271404 | C2 | semidirect |
| 7. #14271374 | C2 | semidirect |
| 8. #14271327 | C2 | semidirect |
| 9. C4×#90773 | C2 | semidirect |
| 10. #14271160 | C2 | semidirect |
| 11. C8×D4×C29 | C2 | semidirect |
| 130. C8×D4 | D29 | semidirect |
| 166. C29 | #3302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271883 | 2 |
| #14271818 | 2 |
| #14271514 | 2 |
| #14271505 | 2 |
| #14271444 | 2 |
| #14271404 | 2 |
| #14271374 | 2 |
| #14271327 | 2 |
| C4×#90773 | 2 |
| #14271160 | 2 |
| C8×D4×C29 | 2 |
| #3302 | 29 |