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. #14271700 | C2 | semidirect |
| 2. #14271564 | C2 | semidirect |
| 3. #14271548 | C2 | semidirect |
| 4. #14271519 | C2 | semidirect |
| 5. #14271401 | C2 | semidirect |
| 7. #14271395 | C2 | semidirect |
| 8. C4×#90784 | C2 | semidirect |
| 9. C4×D232 | C2 | semidirect |
| 10. C4×C8×D29 | C2 | semidirect |
| 11. C4×Q16×C29 | C2 | semidirect |
| 121. C4×Q16 | D29 | semidirect |
| 157. C29 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271700 | 2 |
| #14271564 | 2 |
| #14271548 | 2 |
| #14271519 | 2 |
| #14271401 | 2 |
| #14271400 | 2 |
| #14271395 | 2 |
| C4×#90784 | 2 |
| C4×D232 | 2 |
| C4×C8×D29 | 2 |
| C4×Q16×C29 | 2 |
| #3168 | 29 |