Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 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. #14271891 | C2 | semidirect |
| 4. #14271514 | C2 | semidirect |
| 5. #14271471 | C2 | semidirect |
| 8. #14271374 | C2 | semidirect |
| 9. C4×Dic116 | C2 | semidirect |
| 11. C8×Q8×C29 | C2 | semidirect |
| 120. C8×Q8 | D29 | semidirect |
| 156. C29 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271891 | 2 |
| #14271886 | 2 |
| #14271518 | 2 |
| #14271514 | 2 |
| #14271471 | 2 |
| #14271444 | 2 |
| #14271386 | 2 |
| #14271374 | 2 |
| C4×Dic116 | 2 |
| C4×#90773 | 2 |
| C8×Q8×C29 | 2 |
| #3364 | 29 |