Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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. Q8×D116 | C2 | semidirect |
| 3. #14271514 | C2 | semidirect |
| 4. #14271495 | C2 | semidirect |
| 5. #14271448 | C2 | semidirect |
| 6. #14271391 | C2 | semidirect |
| 7. #14271368 | C2 | semidirect |
| 8. #14271300 | C2 | semidirect |
| 9. C8×D116 | C2 | semidirect |
| 10. #103×D29 | C2 | semidirect |
| 11. C4×SD16×C29 | C2 | semidirect |
| 80. Q8×C29 | #41 | semidirect |
| 94. D116 | SD16 | semidirect |
| 132. C4×SD16 | D29 | semidirect |
| 169. C29 | #3298 | semidirect |
| 213. Q8 | #90805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D116 | 2 |
| #14271818 | 2 |
| #14271514 | 2 |
| #14271495 | 2 |
| #14271448 | 2 |
| #14271391 | 2 |
| #14271368 | 2 |
| #14271300 | 2 |
| C8×D116 | 2 |
| #103×D29 | 2 |
| C4×SD16×C29 | 2 |
| #3298 | 29 |