Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
308 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 2. #14271511 | C2 | semidirect |
| 3. #14271365 | C2 | semidirect |
| 4. #14270906 | C2 | semidirect |
| 5. D4⋊#6597 | C2 | semidirect |
| 6. #14270890 | C2 | semidirect |
| 7. C29×#474 | C2 | semidirect |
| 10. C29×C4⋊Q8 | C22 | semidirect |
| 19. C29×C4⋊C8 | C22 | semidirect |
| 23. C4⋊#6597 | C22 | semidirect |
| 24. C4×#6597 | C22 | semidirect |
| 61. D4×C29 | SD16 | semidirect |
| 106. #474 | D29 | semidirect |
| 120. C4⋊Q8 | C2×D29 | semidirect |
| 129. C4⋊C8 | C2×D29 | semidirect |
| 134. C29 | #1639 | semidirect |
| 180. D4 | #90784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D116 | 2 |
| #14271511 | 2 |
| #14271365 | 2 |
| #14270906 | 2 |
| D4⋊#6597 | 2 |
| #14270890 | 2 |
| C29×#474 | 2 |
| #1639 | 29 |