Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
392 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 139 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×Dic58 | C2 | semidirect |
| 3. #14271510 | C2 | semidirect |
| 4. #14271454 | C2 | semidirect |
| 5. #14271364 | C2 | semidirect |
| 6. C4×#90773 | C2 | semidirect |
| 7. C8×Q8×C29 | C2 | semidirect |
| 44. Q8×C29 | SD16 | semidirect |
| 58. Dic58 | #41 | semidirect |
| 78. C8×Q8 | D29 | semidirect |
| 100. C29 | #3362 | semidirect |
| 124. Q8 | #90773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic58 | 2 |
| #14271835 | 2 |
| #14271510 | 2 |
| #14271454 | 2 |
| #14271364 | 2 |
| C4×#90773 | 2 |
| C8×Q8×C29 | 2 |
| #3362 | 29 |