Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #14271898 | C2 | semidirect |
| 2. #14271552 | C2 | semidirect |
| 3. #14271547 | C2 | semidirect |
| 4. #14271386 | C2 | semidirect |
| 5. #14271379 | C2 | semidirect |
| 6. #14271359 | C2 | semidirect |
| 7. #14271265 | C2 | semidirect |
| 8. C4×D232 | C2 | semidirect |
| 9. C29×#446 | C2 | semidirect |
| 110. #446 | D29 | semidirect |
| 143. C29 | #3403 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271898 | 2 |
| #14271552 | 2 |
| #14271547 | 2 |
| #14271386 | 2 |
| #14271379 | 2 |
| #14271359 | 2 |
| #14271265 | 2 |
| C4×D232 | 2 |
| C29×#446 | 2 |
| #3403 | 29 |